Examkin

Financial Arithmetic

138 soru

Tüm türler138Çoktan seçmeli70Sayısal32Eşleştirme5Sıralama3Boşluk doldurma28
Soru 81Soru →

A graphic designer places $8,000\$8,000 into a high-yield savings certificate that pays an annual simple interest rate of 4.5%4.5\%. Upon maturity, the account has generated exactly $270\$270 in interest. How many months was the money invested?

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Cevap: 9

Cevap

The money was invested for exactly 9 months.
The investment earns $360\$360 in a full year ($8,000×0.045=$360\$8,000 \times 0.045 = \$360). Since the actual interest earned is $270\$270, the time in years is 270/360270 / 360, which simplifies to 3/43/4 or 0.750.75 years. Multiplying 0.750.75 years by 1212 months per year gives exactly 99 months.

Adım Adım Çözüm

1
Identify the given variables and the simple interest formula.
Principal (PP) = $8,000\$8,000, Interest (II) = $270\$270, Rate (rr) = 4.5%4.5\% or 0.0450.045. The formula is I=P×r×tI = P \times r \times t.
Setting up the standard formula is the first step to isolate and find the unknown time variable.
2
Calculate the amount of interest earned in one full year.
$8,000×0.045=$360\$8,000 \times 0.045 = \$360 per year.
Finding the annual interest provides the denominator needed to determine what fraction of a year the money was invested.
3
Divide the actual interest earned by the annual interest to find the time in years.
$270/$360=0.75\$270 / \$360 = 0.75 years.
The ratio of earned interest to annual interest gives the exact time the money remained in the account in years.
4
Convert the time from years into months.
0.75 years×12 months/year=9 months0.75 \text{ years} \times 12 \text{ months/year} = 9 \text{ months}.
The question specifically asks for the time duration in months, requiring a final unit conversion.

Anahtar Kavram

Calculating the time duration of an investment using the simple interest formula and converting the resulting fractional year into months.
Tahmini Süre:1m 30s
Soru 82Soru →

An events coordinator receives a guaranteed weekly salary of $900\$900. On top of this, the coordinator is paid a 4%4\% commission on the first $15,000\$15,000 of event contracts secured each week, and a 7%7\% commission on the value of any contracts above $15,000\$15,000. If the coordinator secures $22,000\$22,000 in event contracts in a single week, what is the coordinator's total gross pay for that week?

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Cevap: $1,990\$1,990

Cevap

$1,990\$1,990
The total gross pay consists of the base salary plus the commission from both tiers. First, calculate the commission on the initial $15,000\$15,000: 4%4\% of $15,000\$15,000 is $600\$600. Next, find the amount eligible for the 7%7\% tier by subtracting $15,000\$15,000 from the total $22,000\$22,000, which leaves $7,000\$7,000. Calculate the commission on this remaining amount: 7%7\% of $7,000\$7,000 is $490\$490. Finally, add the guaranteed salary and both commission amounts: $900+$600+$490=$1,990\$900 + \$600 + \$490 = \$1,990.

Adım Adım Çözüm

1
Calculate the commission earned on the first tier.
4%4\% of $15,000=0.04×15,000=$600\$15,000 = 0.04 \times 15,000 = \$600
The coordinator earns a 4%4\% commission on the first $15,000\$15,000 of contracts.
2
Determine the value of contracts in the second tier.
$22,000−$15,000=$7,000\$22,000 - \$15,000 = \$7,000
The 7%7\% commission applies only to the amount exceeding the initial $15,000\$15,000.
3
Calculate the commission earned on the second tier.
7%7\% of $7,000=0.07×7,000=$490\$7,000 = 0.07 \times 7,000 = \$490
Multiply the remaining contract value by the 7%7\% rate.
4
Calculate the total gross pay.
$900+$600+$490=$1,990\$900 + \$600 + \$490 = \$1,990
Add the guaranteed weekly salary to both commission amounts to find the total earnings.

Anahtar Kavram

Wages, Salaries, and Commissions
Tahmini Süre:1m 30s
Soru 83Soru →

An inside sales representative is compensated with a fixed weekly base pay of $450\$450. Furthermore, for any weekly sales volume surpassing an $8,000\$8,000 threshold, they receive a 5%5\% commission on the excess amount. If the representative generated $14,500\$14,500 in sales last week, what was their total gross pay for that week, in dollars?

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Cevap: 775

Cevap

775
The correct answer is determined by first finding the sales amount eligible for commission (14,500−14,500 - 8,000 = 6,500).Next,calculatethe56,500). Next, calculate the 5% commission on this excess amount ( 6,500 \times 0.05 = 325).Finally,addthiscommissiontothefixedweeklybasepaytofindthetotalgrosspay(325). Finally, add this commission to the fixed weekly base pay to find the total gross pay ( 450 + 325=325 = 775).

Adım Adım Çözüm

1
Determine the portion of sales subject to the commission rate.
$14,500−$8,000=$6,500\$14,500 - \$8,000 = \$6,500
The commission is only applied to the sales volume that surpasses the $8,000 threshold.
2
Calculate the commission earned on the excess sales.
$6,500×0.05=$325\$6,500 \times 0.05 = \$325
The representative earns 5% on the eligible sales amount.
3
Calculate the total gross pay.
$450+$325=$775\$450 + \$325 = \$775
Total gross pay is the sum of the fixed base pay and the earned commission.

Anahtar Kavram

Calculating total gross pay using a base salary and a commission rate applied to sales above a specified threshold.
Soru 84Soru →

A retiree wants to earn exactly 1,8001,800 in simple interest over a period of 15 months to help pay for a vacation. A local credit union offers a short-term investment account with an annual simple interest rate of 4%4\%. Assuming no other deposits or withdrawals are made, how much money must the retiree deposit initially to reach this interest goal?

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Cevap: $36,000

Cevap

$36,000
To find the initial deposit (principal), the simple interest formula I=P×R×TI = P \times R \times T must be rearranged to solve for PP, yielding P=IR×TP = \frac{I}{R \times T}. Because the rate is an annual percentage, the 15-month period must first be converted into years (15/12=1.2515 / 12 = 1.25 years). Substituting the given values gives P=18000.04×1.25P = \frac{1800}{0.04 \times 1.25}, which simplifies to 1800/0.05=360001800 / 0.05 = 36000. Therefore, an initial deposit of 36,00036,000 is required.

Adım Adım Çözüm

1
Convert the time duration from months to years.
T=1512=1.25T = \frac{15}{12} = 1.25 years
The interest rate is provided as an annual rate, so the time factor in the simple interest formula must also be expressed in years.
2
Set up the simple interest formula with the known values.
I=P×R×T→1800=P×0.04×1.25I = P \times R \times T \rightarrow 1800 = P \times 0.04 \times 1.25
The formula connects the interest earned (II) to the principal (PP), rate (RR), and time (TT).
3
Solve for the unknown principal (PP).
P=18000.04×1.25=18000.05=36000P = \frac{1800}{0.04 \times 1.25} = \frac{1800}{0.05} = 36000
Isolating PP determines the initial deposit required to reach the interest goal.

Anahtar Kavram

Calculating the initial principal using the simple interest formula by isolating the principal variable and properly converting time into years.
Soru 85Soru →

A college student invests $2,500\$2,500 of their scholarship money into a bank savings certificate that pays an annual simple interest rate of 3.6%3.6\%. How many months will it take for the investment to earn exactly $135\$135 in interest?

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Cevap: 18

Cevap

18
The simple interest formula is I=P×r×tI = P \times r \times t. Substituting the given values gives 135=2500×0.036×t135 = 2500 \times 0.036 \times t. Solving for tt yields 1.51.5 years. Multiplying by 12 converts this to exactly 18 months.

Adım Adım Çözüm

1
Identify the simple interest formula and the given values.
I=P×r×tI = P \times r \times t, where I=$135I = \$135, P=$2,500P = \$2,500, and r=0.036r = 0.036.
To set up the equation to solve for the unknown time variable.
2
Substitute the values into the formula and simplify.
135=2500×0.036×t135 = 2500 \times 0.036 \times t, which simplifies to 135=90t135 = 90t.
To isolate the term with the unknown variable.
3
Solve for the time tt in years.
t=135/90=1.5t = 135 / 90 = 1.5 years.
The standard simple interest formula calculates time in years.
4
Convert the time from years to months.
1.5×12=181.5 \times 12 = 18 months.
The question specifically asks for the duration in months.

Anahtar Kavram

Simple Interest
Soru 86Soru →

A corporate travel agent earns a fixed base salary of $2,400\$2,400 per month, plus a 6%6\% commission on the total value of all bookings she makes. If her goal is to earn exactly $4,200\$4,200 in gross pay this month, what must be the total value of her bookings?

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Cevap: $30,000\$30,000

Cevap

$30,000\$30,000
The total gross pay consists of the base salary plus the commission. By subtracting the base salary of $2,400\$2,400 from the target gross pay of $4,200\$4,200, the required commission is determined to be $1,800\$1,800. Since the commission rate is 6%6\%, dividing $1,800\$1,800 by 0.060.06 yields the total required bookings of $30,000\$30,000.

Adım Adım Çözüm

1
Determine the amount of pay that must come from commission.
$4,200−$2,400=$1,800\$4,200 - \$2,400 = \$1,800
The base salary is a fixed amount, so the remainder of the target gross pay must be earned through commissions.
2
Convert the commission percentage to a decimal.
6%=0.066\% = 0.06
Percentages must be converted to decimals before they can be used in division calculations.
3
Calculate the total bookings required to earn the target commission.
$1,800÷0.06=$30,000\$1,800 \div 0.06 = \$30,000
Since commission is calculated as (Bookings × Commission Rate), dividing the required commission by the rate gives the required bookings.

Anahtar Kavram

Calculating required sales to meet a target income when given a base salary and a commission rate.
Soru 87Soru →

A small business owner takes out a loan of $15,000\$15,000 to repair commercial equipment. After exactly 8 months, the loan is paid off with a single payment of $15,900\$15,900. Assuming simple interest is applied, what is the annual interest rate on the loan?

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Cevap: 9%9\%

Cevap

The annual simple interest rate on the loan is 9%9\%.
To find the annual interest rate, we first determine the total interest paid by subtracting the principal from the total payment ($15,900−$15,000=$900\$15,900 - \$15,000 = \$900). Next, we convert the 8-month term into years by dividing by 12, which gives 2/32/3 of a year. Plugging these into the simple interest formula, I=P×R×TI = P \times R \times T, gives 900=15,000×R×(2/3)900 = 15,000 \times R \times (2/3). Simplifying the right side yields 900=10,000×R900 = 10,000 \times R. Dividing both sides by 10,000 results in R=0.09R = 0.09, or 9%9\%.

Adım Adım Çözüm

1
Calculate the total amount of interest paid.
$15,900−$15,000=$900\$15,900 - \$15,000 = \$900
The simple interest formula requires the interest amount, which is the difference between the total payoff amount and the original principal.
2
Convert the loan duration from months into a fraction of a year.
8 months=812 year=23 year8 \text{ months} = \frac{8}{12} \text{ year} = \frac{2}{3} \text{ year}
Annual simple interest rates require the time variable (TT) to be expressed in years.
3
Substitute the known values into the simple interest formula (I=P×R×TI = P \times R \times T) and solve for the rate (RR).
$900=$15,000×R×23\$900 = \$15,000 \times R \times \frac{2}{3}
$900=$10,000×R\$900 = \$10,000 \times R
R=90010,000=0.09=9%R = \frac{900}{10,000} = 0.09 = 9\%
Isolating RR provides the annual interest rate in decimal form, which is then converted to a percentage.

Anahtar Kavram

Calculating the annual simple interest rate when given the principal, the total maturity amount, and a fractional time period in months.
Soru 88Soru →

A wholesale electronics representative earns a guaranteed weekly base salary of $800\$800. In addition to the base salary, he earns a 5%5\% commission on any weekly sales that exceed a $2,000\$2,000 quota. If his total sales for the week were $6,500\$6,500, what was his total gross pay for the week?

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Cevap: $1,025\$1,025

Cevap

$1,025\$1,025
The total gross pay is the sum of the base salary and the earned commission. First, subtract the quota from total sales to find the commissionable amount: $6,500−$2,000=$4,500\$6,500 - \$2,000 = \$4,500. Next, calculate the 5%5\% commission on this amount: $4,500×0.05=$225\$4,500 \times 0.05 = \$225. Finally, add the commission to the base salary: $800+$225=$1,025\$800 + \$225 = \$1,025.

Adım Adım Çözüm

1
Determine the amount of sales eligible for commission by subtracting the quota from total sales.
$6,500−$2,000=$4,500\$6,500 - \$2,000 = \$4,500
The 5%5\% commission is only earned on sales that exceed the $2,000\$2,000 quota.
2
Calculate the commission amount by converting 5%5\% to a decimal and multiplying it by the eligible sales.
0.05×$4,500=$2250.05 \times \$4,500 = \$225
This determines the additional earnings from sales performance.
3
Add the calculated commission to the guaranteed base salary to find the total gross pay.
$800+$225=$1,025\$800 + \$225 = \$1,025
Total gross pay is the sum of all fixed and variable earnings.

Anahtar Kavram

Calculating total gross pay involving a base salary and a threshold-based commission.
Soru 89Soru →

To fund a certification course, a network administrator invested a specific amount of money into a standard savings account yielding 5%5\% annual simple interest. After leaving the funds untouched for 3030 months, the investment generated exactly $375\$375 in interest alone. What was the initial amount deposited into the account?

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Cevap: 3000

Cevap

The initial amount deposited was $3,000.
The principal is found by dividing the interest earned by the product of the annual interest rate and the time in years. Converting 3030 months to 2.52.5 years and using the 5%5\% rate as 0.050.05, the calculation is 375÷(0.05×2.5)=3000375 \div (0.05 \times 2.5) = 3000.

Adım Adım Çözüm

1
Identify the given variables for the simple interest formula.
I=375I = 375, r=0.05r = 0.05, t=30t = 30 months.
The formula requires these values to solve for the unknown principal PP.
2
Convert the time period from months to years.
t=3012=2.5t = \frac{30}{12} = 2.5 years.
The given interest rate is an annual rate, so the time must also be expressed in years.
3
Set up the simple interest equation.
375=P×0.05×2.5375 = P \times 0.05 \times 2.5
Using the standard simple interest formula I=P×r×tI = P \times r \times t.
4
Solve for the principal PP.
P=3750.125=3000P = \frac{375}{0.125} = 3000
Isolating PP provides the final initial deposit amount.

Anahtar Kavram

Calculating the principal using the simple interest formula over a fractional year term.
Soru 90Soru →

Match each retail transaction scenario to its corresponding profit or loss percentage.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

Purchase a pair of shoes for 5050 dollars and sell them for 7575 dollars.
Purchase a bicycle for 200200 dollars and sell it for 150150 dollars.
Purchase a jacket for 100100 dollars and sell it for 120120 dollars.
Purchase a book for 1010 dollars and sell it for 99 dollars.

Eşleşmeler

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Cevap

Shoes map to 50%50\% profit; Bicycle maps to 25%25\% loss; Jacket maps to 20%20\% profit; Book maps to 10%10\% loss.
Each scenario is correctly evaluated by finding the absolute difference between cost and selling price, dividing that difference by the original cost price, and converting the result to a percentage.

Adım Adım Çözüm

1
Determine if each transaction resulted in a profit or a loss.
Shoes and jacket are profits; bicycle and book are losses.
If selling price is greater than cost, it is a profit. If selling price is less than cost, it is a loss.
2
Calculate the dollar amount of the profit or loss for each item.
Shoes: 2525 dollars profit, Bicycle: 5050 dollars loss, Jacket: 2020 dollars profit, Book: 11 dollar loss.
Profit or loss equals the absolute difference between selling price and cost price.
3
Divide the profit or loss amount by the original cost price, then multiply by 100100 to find the percentage.
Shoes: (25/50)×100=50%(25/50) \times 100 = 50\%; Bicycle: (50/200)×100=25%(50/200) \times 100 = 25\%; Jacket: (20/100)×100=20%(20/100) \times 100 = 20\%; Book: (1/10)×100=10%(1/10) \times 100 = 10\%.
Percentages must always be calculated relative to the original cost price.

Anahtar Kavram

Calculating percentage profit or loss by comparing the change in value to the original cost price.
Soru 91Soru →

Determine the total amount saved and the final pre-tax price for the successive discounts described below.

Aşağıdaki boşlukları doldurun

An auto parts store lists a set of all-terrain tires for a regular price of $800\$800. During a holiday event, the tires are marked down by 15%15\%. A customer applies a military discount that takes an additional 10%10\% off the already reduced sale price. The customer saves a total of $\$fromtheregularprice,resultinginafinalpre−taxpriceof from the regular price, resulting in a final pre-tax price of \$$.
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Cevap

The total savings is $188\$188, and the final price is $612\$612.
To find successive discounts, each percentage must be applied to the current reduced price. First, a 15%15\% discount on $800\$800 reduces the price by $120\$120, making it $680\$680. Then, a 10%10\% discount is applied to the $680\$680 sale price, which reduces it by another $68\$68. The final price is $680−$68=$612\$680 - \$68 = \$612. The total amount saved is the sum of both discounts, $120+$68=$188\$120 + \$68 = \$188.

Adım Adım Çözüm

1
Calculate the first discount amount.
$800×0.15=$120\$800 \times 0.15 = \$120
Find the dollar value of the initial 15%15\% holiday mark-down.
2
Calculate the intermediate sale price.
$800−$120=$680\$800 - \$120 = \$680
Subtract the first discount from the regular price to find the new base price for the second discount.
3
Calculate the second discount amount.
$680×0.10=$68\$680 \times 0.10 = \$68
Apply the 10%10\% military discount to the intermediate sale price, not the original price.
4
Determine the total savings and final price.
Total savings: $120+$68=$188\$120 + \$68 = \$188. Final price: $800−$188=$612\$800 - \$188 = \$612.
Combine both discount amounts to find the total saved, and subtract from the original price to find the final price.

Anahtar Kavram

Calculating successive discounts requires applying the second percentage to the newly reduced price, rather than adding the percentages together.
Tahmini Süre:1m 30s
Soru 92Soru →

A customer is purchasing a winter coat that has an original price of $140\$140. The store offers a 25%25\% discount on the coat. After the discount is applied, a 6%6\% sales tax is added to the purchase. What is the final total cost of the winter coat?

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Cevap: $111.30\$111.30

Cevap

The final total cost of the winter coat is $111.30\$111.30.
The correct answer accurately calculates the discounted price first ($105\$105), and then correctly applies the 6%6\% sales tax to that new, lower amount ($105×1.06=$111.30\$105 \times 1.06 = \$111.30).

Adım Adım Çözüm

1
Calculate the discount amount.
$140×0.25=$35\$140 \times 0.25 = \$35
To find how much money will be taken off the original price, multiply the original price by the discount percentage.
2
Determine the discounted sale price.
$140−$35=$105\$140 - \$35 = \$105
Subtract the discount amount from the original price to find the price before tax.
3
Calculate the sales tax on the discounted price.
$105×0.06=$6.30\$105 \times 0.06 = \$6.30
Sales tax is applied only to the final sale price, not the original sticker price.
4
Calculate the final total cost.
$105+$6.30=$111.30\$105 + \$6.30 = \$111.30
Add the sales tax amount to the discounted sale price to find the final amount paid at the register.

Anahtar Kavram

Discounts and Sale Prices
Soru 93Soru →

An electronics store is liquidating its marine equipment inventory. A high-frequency boat radar system is marked down by 20%20\% from its original price. During a special weekend clearance event, an additional 10%10\% is taken off the already discounted price. If the final sale price of the radar system is $360\$360, what was the original price of the system in dollars?

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Cevap: 500

Cevap

The original price of the radar system was $500.
The correct answer is found by setting up an equation with successive multipliers for each discount phase: x×0.80×0.90=360x \times 0.80 \times 0.90 = 360. Simplifying the left side yields 0.72x=3600.72x = 360, and dividing by 0.720.72 correctly identifies the original price as $500.

Adım Adım Çözüm

1
Set up an expression for the price after the first discount.
0.80x0.80x
A 20%20\% discount means the buyer pays 100%−20%=80%100\% - 20\% = 80\% of the original price xx.
2
Set up an expression for the price after the second discount.
0.72x0.72x
An additional 10%10\% discount means the buyer pays 90%90\% of the already discounted price. Multiplying 0.90×0.80x0.90 \times 0.80x gives 0.72x0.72x.
3
Set the final expression equal to the sale price and solve for the original price.
0.72x=360⇒x=5000.72x = 360 \Rightarrow x = 500
This isolates the original price, xx, finding the initial value before any markdowns.

Anahtar Kavram

Calculating successive discounts and setting up an equation to find the original pre-sale price.
Soru 94Soru →

Calculate the total gross earnings based on the given compensation structure.

Aşağıdaki boşlukları doldurun

A medical supplies sales representative earns a weekly base salary of $600\$600. She also earns a 4%4\% commission on her first $10,000\$10,000 in sales for the week, and a 7%7\% commission on any sales amount exceeding $10,000\$10,000. If she achieves $18,000\$18,000 in total sales this week, her total gross earnings will be $\$$.
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Cevap

1,560
To find the total gross earnings, we must add the base salary to the commissions earned from each tier. The base salary is $600\$600. The first commission tier is 4%4\% of the first $10,000\$10,000, which is $400\$400. The second tier is 7%7\% of the remaining $8,000\$8,000 in sales (since $18,000−$10,000=$8,000\$18,000 - \$10,000 = \$8,000), which is $560\$560. Adding these three components together gives $600+$400+$560=$1,560\$600 + \$400 + \$560 = \$1,560.

Adım Adım Çözüm

1
Identify the fixed base salary.
The base salary is $600\$600.
This is a guaranteed amount earned regardless of the sales volume achieved.
2
Calculate the commission on the first $10,000\$10,000 of sales.
0.04×$10,000=$4000.04 \times \$10,000 = \$400.
The representative earns a 4%4\% commission on all sales up to the $10,000\$10,000 threshold.
3
Determine the amount of sales that exceeds the $10,000\$10,000 threshold.
$18,000−$10,000=$8,000\$18,000 - \$10,000 = \$8,000.
The higher commission rate of 7%7\% only applies to the portion of sales above $10,000\$10,000.
4
Calculate the commission on the sales exceeding $10,000\$10,000.
0.07×$8,000=$5600.07 \times \$8,000 = \$560.
This applies the 7%7\% rate to the remaining $8,000\$8,000 in sales.
5
Add the base salary and all commissions to find the total gross earnings.
$600+$400+$560=$1,560\$600 + \$400 + \$560 = \$1,560.
Total gross earnings are the sum of the fixed base salary and all variable commission tiers.

Anahtar Kavram

Calculating total gross earnings using a combination of a fixed base salary and a tiered commission structure.
Soru 95Soru →

A landscaping company is purchasing a bulk order of premium grass seed. The wholesale price of the order is $550\$550. The supplier offers a 20%20\% commercial discount on the order. After the discount is applied, a 5%5\% sales tax is added. What is the final total cost of the grass seed order?

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Cevap: $462.00\$462.00

Cevap

The final total cost of the grass seed order is $462.00\$462.00.
The correct answer is found by completing the calculation in two distinct steps. First, apply the 20%20\% discount to the original $550\$550 price ($550×0.80=$440\$550 \times 0.80 = \$440). Second, calculate the 5%5\% sales tax on the new $440\$440 balance and add it to the cost ($440×1.05=$462.00\$440 \times 1.05 = \$462.00).

Adım Adım Çözüm

1
Calculate the discount amount by finding 20%20\% of $550\$550.
$550×0.20=$110\$550 \times 0.20 = \$110
The commercial discount reduces the original wholesale price by a percentage.
2
Subtract the discount amount from the original price to find the sale price.
$550−$110=$440\$550 - \$110 = \$440
This establishes the actual price of the grass seed before sales tax is applied.
3
Calculate the 5%5\% sales tax on the discounted sale price.
$440×0.05=$22\$440 \times 0.05 = \$22
Sales tax must be applied to the final sale price, not the original sticker price.
4
Add the sales tax to the sale price to find the final total cost.
$440+$22=$462.00\$440 + \$22 = \$462.00
The final cost includes both the discounted price and the applicable tax.

Anahtar Kavram

Calculating multi-step financial arithmetic problems involving sequential discounts and sales taxes.
Soru 96Soru →

A ship's culinary specialist is ordering bulk ground coffee. A 1212-ounce bag of coffee costs $5.40\$5.40. A 33-pound container of the same coffee costs $18.00\$18.00. How much money is saved per pound by purchasing the 33-pound container instead of multiple 1212-ounce bags?

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Cevap: $1.20\$1.20

Cevap

$1.20\$1.20
The correct savings is found by determining the unit price of each option for exactly one pound and subtracting them. The 1212-ounce bag costs $0.45\$0.45 per ounce, which equates to $7.20\$7.20 per pound (0.45×160.45 \times 16). The 33-pound container costs $6.00\$6.00 per pound (18.00÷318.00 \div 3). Subtracting the container's unit price from the bag's unit price yields a savings of $1.20\$1.20 per pound.

Adım Adım Çözüm

1
Calculate the price per pound for the 33-pound container.
$18.00÷3=$6.00\$18.00 \div 3 = \$6.00 per pound.
To find the baseline unit price of the bulk option for comparison.
2
Determine the cost per ounce of the 1212-ounce bag.
$5.40÷12=$0.45\$5.40 \div 12 = \$0.45 per ounce.
To find the base unit rate of the smaller bags before scaling up to a full pound.
3
Calculate the price per pound for the 1212-ounce bag.
$0.45×16=$7.20\$0.45 \times 16 = \$7.20 per pound.
Because there are 1616 ounces in a pound, multiplying the cost per ounce by 1616 gives the comparable unit price.
4
Find the difference in price per pound.
$7.20−$6.00=$1.20\$7.20 - \$6.00 = \$1.20.
Subtracting the unit price of the bulk container from the unit price of the bags determines the exact savings per pound.

Anahtar Kavram

Unit Price Comparisons across different measurement scales
Tahmini Süre:1m 30s
Soru 97Soru →

An aviation logistics specialist is sourcing a specific synthetic lubricant for aircraft maintenance. A local supplier sells the lubricant in 11-quart bottles for $5.50\$5.50 each. A wholesale distributor sells the same lubricant in 55-gallon drums for $95.00\$95.00 per drum. How much money is saved per gallon by purchasing the 55-gallon drum instead of the individual 11-quart bottles?

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Cevap: 3

Cevap

3
To find the savings per gallon, both purchase options must be converted to a per-gallon rate. Because there are 4 quarts in a US gallon, the 1-quart bottles effectively cost $5.50×4=$22.00\$5.50 \times 4 = \$22.00 per gallon. The 5-gallon drum costs $95.00÷5=$19.00\$95.00 \div 5 = \$19.00 per gallon. The difference in price is $22.00−$19.00=$3.00\$22.00 - \$19.00 = \$3.00 saved per gallon.

Adım Adım Çözüm

1
Calculate the price per gallon for the 1-quart bottles.
$5.50×4=$22.00\$5.50 \times 4 = \$22.00 per gallon.
There are 4 quarts in a gallon, so the unit price must be scaled up to match the gallon comparison unit.
2
Calculate the price per gallon for the 5-gallon drum.
$95.00÷5=$19.00\$95.00 \div 5 = \$19.00 per gallon.
The total cost of the drum must be divided by its volume in gallons to find the unit price.
3
Calculate the difference between the two unit prices.
$22.00−$19.00=$3.00\$22.00 - \$19.00 = \$3.00
Subtracting the lower unit price from the higher unit price reveals the savings per gallon.

Anahtar Kavram

Calculating and comparing unit rates involving US customary capacity conversions.
Soru 98Soru →

A carpenter is purchasing a commercial-grade table saw. The original price of the table saw is $850\$850. The store offers a 20%20\% discount on all power tools. After the discount is applied, a 5%5\% sales tax is added to the purchase price. What is the final total amount the carpenter pays for the table saw?

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Cevap: $714.00\$714.00

Cevap

$714.00\$714.00
To find the final price, first determine the sale price by taking 20%20\% off the original $850\$850. Since 20%20\% of $850\$850 is $170\$170, the discounted price is $680\$680. Next, apply the 5%5\% sales tax to the new sale price of $680\$680. The tax is 0.05×$680=$340.05 \times \$680 = \$34. Adding the tax to the sale price gives the final total of $714.00\$714.00.

Adım Adım Çözüm

1
Calculate the discount amount.
$170\$170
The discount is 20%20\% of the original price: 0.20×$850=$1700.20 \times \$850 = \$170.
2
Determine the discounted sale price.
$680\$680
Subtract the discount amount from the original price: $850−$170=$680\$850 - \$170 = \$680.
3
Calculate the sales tax amount on the sale price.
$34\$34
The tax is 5%5\% of the discounted price: 0.05×$680=$340.05 \times \$680 = \$34.
4
Calculate the final total amount.
$714.00\$714.00
Add the sales tax to the sale price: $680+$34=$714\$680 + \$34 = \$714.

Anahtar Kavram

Discounts and Sale Prices
Soru 99Soru →

A construction battalion is procuring wood varnish for a barracks renovation. A supplier sells the varnish in a 55-gallon bucket for $120.00\$120.00. Alternatively, the same varnish is sold in 11-quart cans for $8.00\$8.00 each. How much money is saved per gallon by purchasing the 55-gallon bucket instead of the 11-quart cans?

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Cevap: \$8.00

Cevap

The 55-gallon bucket saves $8.00\$8.00 per gallon compared to the 11-quart cans.
To accurately compare the costs, both options must be calculated as a price per gallon. The 55-gallon bucket costs $120.00\$120.00, which breaks down to $120.00÷5=$24.00\$120.00 \div 5 = \$24.00 per gallon. For the second option, because there are 44 quarts in 11 gallon, the price per gallon is 4×$8.00=$32.004 \times \$8.00 = \$32.00. The savings per gallon is the difference between these two unit rates: $32.00−$24.00=$8.00\$32.00 - \$24.00 = \$8.00.

Adım Adım Çözüm

1
Calculate the unit price per gallon for the 55-gallon bucket.
$120.00÷5=$24.00\$120.00 \div 5 = \$24.00 per gallon
This establishes the baseline unit price for the bulk option.
2
Convert the price of the 11-quart cans into a price per gallon.
Since there are 44 quarts in a gallon, 4×$8.00=$32.004 \times \$8.00 = \$32.00 per gallon
Both unit prices must be in the same measurement (gallons) to make an accurate comparison.
3
Subtract the bucket's gallon price from the cans' gallon price to find the savings.
$32.00−$24.00=$8.00\$32.00 - \$24.00 = \$8.00
The question asks for the money saved per gallon by choosing the bucket.

Anahtar Kavram

Comparing unit prices requiring unit conversions
Soru 100Soru →

A bakery owner is purchasing a new commercial dough mixer. The original price of the mixer is $1,500\$1,500. The restaurant supply store is running a promotional sale offering a 20%20\% discount on all equipment. Additionally, the owner receives an extra 10%10\% discount on the sale price for paying directly through a business bank transfer. What is the final sale price of the dough mixer in dollars?

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Cevap: 1080

Cevap

The final sale price of the dough mixer is $1,080\$1,080.
To find the final price after successive discounts, each discount must be applied sequentially to the updated balance. First, applying the 20%20\% discount to the original $1,500\$1,500 price reduces it by $300\$300, resulting in an intermediate sale price of $1,200\$1,200. The subsequent 10%10\% discount is then applied to this new $1,200\$1,200 balance, taking off an additional $120\$120. Subtracting $120\$120 from $1,200\$1,200 yields a final price of $1,080\$1,080.

Adım Adım Çözüm

1
Calculate the amount of the first discount.
$1,500×0.20=$300\$1,500 \times 0.20 = \$300
The promotional discount applies to the original base price.
2
Determine the intermediate sale price after the first discount.
$1,500−$300=$1,200\$1,500 - \$300 = \$1,200
Subtracting the discount from the original price gives the new price before further markdowns.
3
Calculate the amount of the second discount.
$1,200×0.10=$120\$1,200 \times 0.10 = \$120
Successive discounts are calculated based on the new reduced sale price, not the original price.
4
Determine the final price after the second discount.
$1,200−$120=$1,080\$1,200 - \$120 = \$1,080
Subtracting the second discount from the intermediate price yields the final amount owed.

Anahtar Kavram

Successive/Chain Discounts
ÖncekiSayfa 5 / 7Sonraki
Financial Arithmetic Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 5 | Examkin