All practice questions

Question 21Question →

A base logistics center is processing a shipment of 2,400 supply crates. Over three days, the following portions of the total shipment were processed:

- Monday: $31.25\%$ of the total shipment
- Tuesday: $\frac{5}{12}$ of the total shipment
- Wednesday: $0.125$ of the total shipment

How many supply crates remain to be processed?

Show answer & explanation

Answer: 350

Answer

350

The total amount processed is found by converting all values to fractions:

31.25\%

becomes

\frac{5}{16}

and

0.125

becomes

\frac{1}{8}

. Adding these to

\frac{5}{12}

using a common denominator of 48 gives

\frac{41}{48}

processed. The remaining

\frac{7}{48}

of the 2,400 total crates equals 350 crates.

Step-by-Step Solution

1

Convert

31.25\%

and

0.125

to fractions.

31.25\% = \frac{5}{16}

and

0.125 = \frac{1}{8}

.

Working in a single format (fractions) is the most precise way to add parts of a whole without losing exact values.

2

Find the least common denominator (LCD) for

\frac{5}{16}

,

\frac{5}{12}

, and

\frac{1}{8}

.

The LCD for 16, 12, and 8 is 48.

Fractions must have the same denominator before they can be added.

3

Convert each fraction to have a denominator of 48 and sum them together.

\frac{15}{48} + \frac{20}{48} + \frac{6}{48} = \frac{41}{48}

This calculates the total fraction of the shipment that has already been processed over the three days.

4

Subtract the processed fraction from 1 to find the remaining fraction.

1 - \frac{41}{48} = \frac{7}{48}

The question asks for the remaining amount of crates, not the completed amount.

5

Multiply the remaining fraction by the total number of crates (2,400).

\frac{7}{48} \times 2400 = 7 \times 50 = 350

This converts the fractional remainder back into the actual physical quantity of crates.

Key Concept

Converting percentages and decimals to fractions to efficiently sum portions of a whole, and applying a fractional remainder to a total quantity.

Question 22Question →

A military dining facility prepares a standard meal using a ratio of $4$ pounds of beef for every $3$ pounds of rice. If the facility uses $24$ pounds of rice for a meal, how many pounds of beef will be needed?

Show answer & explanation

Answer: 32

Answer

32

Because the required ratio of beef to rice is

4:3

, every

3

pounds of rice requires

4

pounds of beef. Since

24

pounds of rice is

8

times the base amount (

24 \div 3 = 8

), the amount of beef must also be scaled by

8

. Multiplying

4

pounds by

8

yields exactly

32

pounds of beef.

Step-by-Step Solution

1

Identify the given ratio and the known actual quantity.

The ratio of beef to rice is

4:3

. The actual amount of rice used is

24

pounds.

Establishing the known values is the first step in solving a proportion.

2

Determine the scale factor between the base ratio and the actual amounts.

24 \div 3 = 8

. The scale factor is

8

.

Since the ratio amount for rice is

3

and the actual amount is

24

, multiplying by

8

scales the ratio up to the actual meal size.

3

Apply the scale factor to the beef portion of the ratio to find the missing quantity.

4 \times 8 = 32

.

To maintain the exact proportional relationship, both parts of the ratio must be multiplied by the same scale factor.

Key Concept

Solving for a missing quantity in a part-to-part ratio using a scale factor.

Estimated Time:1m 0s

Question 23Question →

A submarine leaves port with enough provisions to feed its standard crew of $120$ personnel for $60$ days. Before departure, $30$ additional mission specialists are assigned to the submarine. If the daily ration per person remains constant, how many days will the provisions last the newly expanded crew?

Show answer & explanation

Answer: 48

Answer

48

Because the total amount of food remains constant, an increase in personnel causes a proportional decrease in the number of days the food will last. The product of personnel and days is constant:

120 \times 60 = 150 \times x

. Solving for

x

gives

7200 / 150 = 48

days.

Step-by-Step Solution

1

Calculate the total amount of provisions available.

120 \text{ personnel} \times 60 \text{ days} = 7200 \text{ person-days}

In an inverse proportion involving resources, the product of the number of consumers and the time the resource lasts represents the constant total resource.

2

Calculate the total number of personnel after the addition.

120 + 30 = 150 \text{ personnel}

The problem states that 30 additional specialists were assigned, so the new crew size is the sum of the original and additional personnel.

3

Calculate the new duration the provisions will last.

7200 \text{ person-days} \div 150 \text{ personnel} = 48 \text{ days}

Dividing the total constant resource by the new number of consumers yields the new time duration.

Key Concept

Inverse Proportions

Estimated Time:1m 0s

Question 24Question →

A mechanic purchases a broken bicycle for $\$40$ at a garage sale. He then buys new tires and a chain for a total of $\$25$ . After repairing the bicycle, he sells it for $\$110$ . What is his total profit, in dollars?

Show answer & explanation

Answer: 45

Answer

45

The total cost is the sum of the purchase price (

\$40

) and the repair parts (

\$25

), which is

\$65

. The profit is found by subtracting this total cost from the selling price (

\$110

), which gives

\$45

.

Step-by-Step Solution

1

Calculate the total cost.

\$40 + \$25 = \$65

The total cost includes the purchase price plus the cost of the repair parts.

2

Calculate the profit.

\$110 - \$65 = \$45

Profit is the difference between the selling price and the total cost.

Key Concept

Profit is calculated by subtracting all associated costs (purchase price plus any overhead or repairs) from the final selling price.

Question 25Question →

A small business hires a contractor to install a new office security system. The initial quote for the work is $800. After negotiating, the business receives a 15% discount on the initial quote. The installation is subject to a 5% local service tax, which is applied to the discounted price. To show appreciation for completing the job ahead of schedule, the business adds a 10% tip calculated from the original$ 800 quote. What is the total amount the business pays in dollars?

Show answer & explanation

Answer: 794

Answer

794

To find the total amount paid, we must sequentially apply the rates to their correct base amounts. First, find the discounted price by subtracting 15% of

800 (

120) from the original quote, yielding

680. Next, calculate the 5% tax on this discounted price (

680 × 0.05 =

34). Then, calculate the 10% tip based on the original quote as specified in the scenario (

800 × 0.10 =

80). The final total is the sum of the discounted price, the tax amount, and the tip amount:

680 +

34 +

80 = $794.

Step-by-Step Solution

1

Calculate the discount amount

$120

The business received a 15% discount on the initial $800 quote.

2

Determine the discounted price

$680

Subtracting the

120 discount from the

800 initial quote gives the new base price for the tax.

3

Calculate the local service tax

$34

The 5% tax is applied to the discounted price of

680 (0.05 ×

680 = $34).

4

Calculate the tip amount

$80

The problem states the 10% tip is specifically based on the original

800 quote (0.10 ×

800 = $80).

5

Calculate the final total

$794

Add the discounted price (

680), the tax (

34), and the tip ($80) to find the total amount paid.

Key Concept

Calculating percentage discounts, taxes, and tips when applied to different base amounts.

Question 26Question →

During a field training exercise, a supply sergeant purchases 8 identical waterproof tarps. If the total cost for all 8 tarps is $\$64.40$ , what is the cost of a single tarp in dollars?

Show answer & explanation

Answer: 8.05

Answer

8.05

The correct answer is found by taking the total cost of all tarps and dividing it by the number of tarps. Dividing

\$64.40

by 8 yields exactly

\$8.05

per tarp.

Step-by-Step Solution

1

Set up the division problem

64.40 \div 8

To find the cost of a single item, divide the total cost by the total quantity.

2

Perform the division

8.05

8 goes into 64 exactly 8 times. Bring down the decimal point. 8 goes into 4 zero times. Bring down the 0 to make 40. 8 goes into 40 exactly 5 times. Thus,

64.40 \div 8 = 8.05

.

Key Concept

Dividing a decimal currency amount by a whole number to find a unit price.

Estimated Time:45s

Question 27Question →

A workshop exhaust fan is connected to a $120\text{ V}$ power supply and consumes $480\text{ W}$ of electric power during normal operation. What is the effective electrical resistance of the fan motor, in ohms ( $\Omega$ )?

Show answer & explanation

Answer: 30

Answer

The effective electrical resistance of the fan motor is

30\,\Omega

.

To find the resistance from voltage and power, determine the current using

I = \frac{P}{V} = \frac{480\text{ W}}{120\text{ V}} = 4\text{ A}

, then use Ohm's law

R = \frac{V}{I} = \frac{120\text{ V}}{4\text{ A}} = 30\,\Omega

. Alternatively, using

R = \frac{V^2}{P}

yields

\frac{120^2}{480} = \frac{14400}{480} = 30\,\Omega

.

Step-by-Step Solution

1

Calculate the electric current flowing through the fan motor using the electrical power formula

P = V \times I

.

I = \frac{P}{V} = \frac{480\text{ W}}{120\text{ V}} = 4\text{ A}

Electric power equals the product of voltage and current, so dividing total wattage by applied voltage determines circuit current.

2

Calculate the resistance using Ohm's law rearranged as

R = \frac{V}{I}

.

R = \frac{120\text{ V}}{4\text{ A}} = 30\,\Omega

Resistance represents the opposition to current flow and is found by dividing the applied voltage by the circuit current.

Key Concept

Relationship between electrical power (

P = IV

) and Ohm's law (

V = IR

)

Estimated Time:1m 0s

Question 28Question →

A small business owner finances the purchase of new office equipment with a $\$3,000$ loan from a local credit union. The loan term is $18$ months. At the end of the term, the owner repays a total of $\$3,360$ , which includes the original loan amount and all accumulated simple interest.

What is the annual simple interest rate (as a percentage) applied to this loan?

Show answer & explanation

Answer: 8

Answer

8

The correct annual simple interest rate is 8%. First, determine the total interest by subtracting the principal from the total repayment (

\$3,360 - \$3,000 = \$360

). Next, convert the 18-month term to years (

18 \div 12 = 1.5 \text{ years}

). Using the simple interest formula

I = PRT

, substitute the values:

360 = 3,000 \times R \times 1.5

. Simplifying this gives

360 = 4,500R

, which means

R = 360 \div 4,500 = 0.08

. Finally, convert

0.08

to a percentage to get

8\%

.

Step-by-Step Solution

1

Calculate the total simple interest earned over the loan term.

Total Interest (I) =

\$3,360 - \$3,000 = \$360

The total repayment amount (A) is the sum of the principal (P) and the interest (I). Therefore, subtracting the principal from the total repayment isolates the interest.

2

Convert the loan duration from months to years.

Time (T) =

18 \text{ months} = 1.5 \text{ years}

The standard simple interest formula

I = PRT

requires time (T) to be expressed in years when calculating an annual interest rate.

3

Apply the simple interest formula and solve for the annual rate (R).

360 = 3000 \times R \times 1.5

360 = 4500 \times R

R = 0.08

Substituting the known values (I, P, T) allows us to isolate and solve for the missing rate variable (R).

4

Convert the decimal rate into a percentage.

0.08 = 8\%

Interest rates are universally expressed as percentages in financial contexts.

Key Concept

Calculating an unknown annual interest rate using the simple interest formula I = PRT, which requires determining the total interest from a final balance and converting time from months to years.

Question 29Question →

A military mess hall receives a shipment of $131 \frac{1}{4}$ pounds of ground beef. The kitchen staff uses $\frac{3}{7}$ of the shipment to prepare lunch. The remaining ground beef is portioned into smaller storage bags that each hold $3 \frac{3}{4}$ pounds for dinner recipes. How many storage bags can be completely filled with the remaining ground beef?

Show answer & explanation

Answer: 20

Answer

20

First, the remaining fraction of beef is determined to be 4/7. Multiplying the total initial weight of 131 1/4 pounds (or 525/4) by 4/7 yields exactly 75 pounds of remaining ground beef. Finally, dividing these 75 pounds by the capacity of each bag, which is 3 3/4 pounds (or 15/4), gives exactly 20 completely filled storage bags.

Step-by-Step Solution

1

Calculate the fraction of the ground beef that remains after lunch.

1 - \frac{3}{7} = \frac{4}{7}

The kitchen staff used 3/7 of the shipment, so 4/7 of the shipment is left for the dinner recipes.

2

Convert the total shipment weight from a mixed number to an improper fraction.

131 \frac{1}{4} = \frac{525}{4}

Converting to an improper fraction makes it easier to multiply by the remaining fraction.

3

Multiply the total weight by the remaining fraction to find the remaining weight.

\frac{4}{7} \times \frac{525}{4} = \frac{525}{7} = 75

pounds

This calculation yields the exact weight of the ground beef available to be portioned into storage bags. Notice that the 4 in the numerator and denominator cancel out.

4

Convert the storage bag capacity from a mixed number to an improper fraction.

3 \frac{3}{4} = \frac{15}{4}

This prepares the divisor for the fraction division step.

5

Divide the remaining weight by the capacity of each storage bag.

75 \div \frac{15}{4} = 75 \times \frac{4}{15} = \frac{300}{15} = 20

bags

Dividing the total available weight by the weight per bag yields the exact number of bags that can be completely filled.

Key Concept

Fraction Multiplication and Division in Context

Estimated Time:1m 30s

Question 30Question →

A supply sergeant initially distributes $2,400$ rounds of specialized training ammunition among three firing squads—Alpha, Bravo, and Charlie—in a ratio of $2:3:5$ , respectively. During the drill, Squad Bravo requests and is issued exactly $180$ additional rounds.

To maintain the exact original $2:3:5$ distribution ratio among the three squads, the sergeant must also issue additional rounds to Alpha and Charlie. How many total additional rounds must be issued to Squads Alpha and Charlie combined to perfectly restore the original ratio?

Show answer & explanation

Answer: 420

Answer

420

By determining that Bravo's 180 additional rounds correspond to its 3 parts in the ratio, we can establish that the proportional increase per part is 60 rounds (180 ÷ 3). Since Alpha and Charlie make up 7 parts combined (2 + 5), they require an additional 7 × 60 = 420 rounds to maintain the ratio.

Step-by-Step Solution

1

Calculate the initial number of rounds representing a single ratio part.

240 rounds per part.

The total of 2,400 rounds is distributed across 2 + 3 + 5 = 10 total parts.

2

Determine Squad Bravo's new total amount of ammunition.

900 rounds.

Bravo initially had 3 parts (3 × 240 = 720). Adding the 180 new rounds brings their total to 720 + 180 = 900 rounds.

3

Calculate the new value of a single ratio part required to maintain the 2:3:5 distribution.

300 rounds per part.

Bravo's new total of 900 rounds must represent its 3 parts in the ratio. Therefore, 900 ÷ 3 = 300.

4

Calculate the total additional rounds needed for Alpha and Charlie combined.

420 rounds.

The proportional increase per ratio part is 300 - 240 = 60 rounds. Alpha and Charlie represent 2 + 5 = 7 parts combined. 7 parts × 60 rounds = 420 rounds.

Key Concept

Dividing quantities based on a given ratio and recalculating proportional parts after a specific adjustment.

Alternative Method

Instead of calculating the initial and final totals for each squad, analyze the proportional change directly. Squad Bravo's allocation increases by 180 rounds. Since Bravo represents 3 parts of the ratio, the increase is 180 ÷ 3 = 60 rounds per ratio part. Squads Alpha and Charlie account for 2 + 5 = 7 ratio parts combined. Therefore, their combined additional requirement is simply 7 parts × 60 rounds/part = 420 rounds.

Estimated Time:2m 30s

Question 31Question →

An air base has a fleet of $200$ transport vehicles. Of these vehicles, $65\%$ are diesel-powered, and the remaining vehicles are electric. Currently, $20\%$ of the diesel-powered vehicles and $40\%$ of the electric vehicles are out of service for routine maintenance. What is the total number of transport vehicles that are currently in service?

Show answer & explanation

Answer: 146

Answer

146

The total number of vehicles in service is found by determining the quantity of each vehicle type, calculating the out-of-service vehicles for each subgroup (26 diesel and 28 electric), and subtracting this total (54) from the overall fleet of 200, resulting in 146 active vehicles.

Step-by-Step Solution

1

Calculate the total number of diesel and electric vehicles in the fleet.

130 diesel vehicles and 70 electric vehicles.

You must establish the correct baseline quantity for each vehicle type before calculating the out-of-service percentages.

2

Calculate the number of vehicles out of service for each type.

26 diesel vehicles and 28 electric vehicles are out of service.

The maintenance rates apply to the specific subgroups, so you take 20% of 130 and 40% of 70.

3

Determine the total number of vehicles that are out of service.

54 vehicles out of service.

Adding the unavailable diesel and electric vehicles gives the total number of inactive vehicles.

4

Subtract the out-of-service vehicles from the total fleet to find the number in service.

146 vehicles in service.

The entire fleet is composed of either in-service or out-of-service vehicles. Subtracting the unavailable ones yields the active fleet.

Key Concept

Calculating successive percentages and determining parts of different subgroups.

Alternative Method

Instead of finding the out-of-service vehicles and subtracting, you can directly calculate the in-service vehicles. Diesel in service = 80% of 130 = 104. Electric in service = 60% of 70 = 42. Total in service = 104 + 42 = 146.

Estimated Time:1m 30s

Question 32Question →

A military maintenance crew is draining a water purification tank for routine cleaning. They manage to drain $\frac{21}{25}$ of the water before the primary pump requires a filter change. What percentage of the water was drained?

Show answer & explanation

Answer: 84

Answer

84

To convert

\frac{21}{25}

to a percentage, multiply both the numerator and the denominator by 4 to reach a denominator of 100. This results in

\frac{84}{100}

, which is exactly 84%.

Step-by-Step Solution

1

Set up the conversion from fraction to percentage.

\frac{21}{25}

This is the proportion of the tank that was drained and needs to be converted.

2

Find an equivalent fraction with a denominator of 100.

\frac{21 \times 4}{25 \times 4} = \frac{84}{100}

Percentages are calculated out of 100. Since 25 is a factor of 100, multiplying by 4 scales the fraction appropriately.

3

Convert the resulting fraction directly to a percentage.

84

A fraction with a denominator of 100 indicates the percentage directly.

Key Concept

Converting a fraction with a easily scalable denominator to a percentage.

Question 33Question →

A logistics officer needs to distribute $150$ tactical backpacks between two infantry squads in a ratio of $2:3$ . How many backpacks will the squad with the smaller share receive?

Show answer & explanation

Answer: 60

Answer

60

To solve the problem, we first determine that the total ratio consists of

5

parts (

2 + 3

). Dividing the

150

total backpacks by

5

parts gives us

30

backpacks for every single part. Because the question asks for the squad with the smaller share, we multiply the

30

backpacks by the smaller ratio number (

2

), which results in

60

backpacks.

Step-by-Step Solution

1

Calculate the total number of parts in the ratio by adding the given values.

2 + 3 = 5

total parts.

This establishes the total number of equal shares the backpacks will be divided into.

2

Determine the number of backpacks in a single part by dividing the total amount by the total parts.

150 \div 5 = 30

backpacks per part.

Finding the unit value allows us to calculate any specific share in the proportion.

3

Calculate the smaller share by multiplying the unit value by the smaller number in the ratio.

30 \times 2 = 60

backpacks.

The question asks for the smaller share, which corresponds to the

2

parts in the

2:3

ratio.

Key Concept

Dividing a total quantity into a given ratio

Question 34Question →

A structural engineering team is mixing a specialized epoxy resin containing base, hardener, and silica filler in a strict ratio of $5:2:1$ by weight. If the team uses exactly $35$ pounds of the base component, what is the total weight, in pounds, of the prepared epoxy mixture?

Show answer & explanation

Answer: 56

Answer

The total weight of the prepared epoxy mixture is 56 pounds.

The components are mixed in a ratio of

5:2:1

, which combines to make a total of

8

parts (

5 + 2 + 1 = 8

). We know the base component accounts for

5

of those parts and weighs

35

pounds. This means a single part weighs

7

pounds (

35 \div 5 = 7

). To find the total mixture weight, multiply the total number of parts (

8

) by the weight of a single part (

7

), resulting in

56

pounds.

Step-by-Step Solution

1

Calculate the total number of parts in the given ratio.

5 + 2 + 1 = 8

total parts.

To establish the relationship between the individual components and the entire mixture.

2

Find the weight equivalent of one ratio part using the known base component.

35 \div 5 = 7

pounds per part.

The base component represents

5

parts of the ratio and weighs

35

pounds, so dividing its weight by its parts gives the unit multiplier.

3

Calculate the total weight of the mixture.

8 \times 7 = 56

pounds.

Multiplying the total number of ratio parts by the weight of a single part yields the overall total weight.

Key Concept

Solving part-to-whole ratio problems by finding the value of a single unit part.

Alternative Method

Calculate the individual weights of the missing components first. Hardener =

2 \times 7 = 14

pounds. Silica =

1 \times 7 = 7

pounds. Then, add these to the given base weight:

35 + 14 + 7 = 56

pounds.

Estimated Time:1m 0s

Question 35Question →

A naval supply ship pumps $3,600$ gallons of fresh water into a destroyer's holding tanks over the course of $4$ hours. At what constant rate, in gallons per hour, is the water being pumped?

Show answer & explanation

Answer: 900

Answer

900

To find the rate in gallons per hour, the total number of gallons (

3,600

) is divided by the total number of hours (

4

), resulting in

900

gallons per hour.

Step-by-Step Solution

1

Identify the total quantity and the total time given in the scenario.

Total quantity =

3,600

gallons. Total time =

4

hours.

A unit rate requires knowing both the total amount and the corresponding time frame.

2

Divide the total gallons by the total hours to find the unit rate.

3,600 \div 4 = 900

Dividing the total amount by the number of hours yields the amount per single hour.

Key Concept

Calculating a basic unit rate by dividing a total quantity by a total time.

Question 36Question →

A developer issues a short-term promissory note to cover construction costs. The note carries an annual simple interest rate of $8\%$ . After $9$ months, the developer repays a total of $\$42,400$ , which includes both the original principal borrowed and the interest earned. What was the original principal amount borrowed, in dollars?

Show answer & explanation

Answer: 40000

Answer

40000

The original principal is found by utilizing the total amount formula for simple interest,

A = P(1 + rt)

, and solving for

P

. By substituting

A = 42,400

,

r = 0.08

, and

t = 0.75

years (from

9

months), the equation simplifies to

1.06P = 42,400

, which yields a principal of $40,000.

Step-by-Step Solution

1

Identify the known variables from the word problem.

Total Amount (

A

) =

42,400

, Rate (

r

) =

8\% = 0.08

, Time (

t

) =

9

months.

Extracting the specific numbers and their corresponding variables is required before applying any formulas.

2

Convert the time duration from months into years.

t = \frac{9}{12} = 0.75

years.

Simple interest formulas require the time unit to match the rate unit, which is annual (

8\%

per year).

3

Apply the total amount simple interest formula and substitute the values.

42,400 = P(1 + 0.08 \times 0.75)

The total amount paid back (

42,400

) includes both the principal (

P

) and the interest (

Prt

), factored out as

P(1 + rt)

.

4

Simplify the equation.

42,400 = P(1 + 0.06) \Rightarrow 42,400 = 1.06P

Multiplying the rate by the time yields the total interest multiplier (

6\%

or

0.06

), adding it to

1

gives the total amount multiplier.

5

Solve for the principal (

P

).

P = \frac{42,400}{1.06} = 40,000

Isolating

P

gives the original amount borrowed. The division can be calculated mentally by noting that

424

is

4 \times 106

.

Key Concept

Solving for Principal in a Simple Interest Total Amount Scenario

Question 37Question →

A furniture restorer buys an antique dining set for $\$250$ . The restorer spends $\$80$ on wood stain and varnish, and pays an upholsterer $\$170$ to repair the chair cushions. After the restoration is complete, the dining set is sold for $\$800$ . What is the restorer's profit as a percentage of their total cost?

Show answer & explanation

Answer: 60

Answer

60%

By summing the initial price and all repair costs, we find the total investment is

500. Subtracting this from the

800 selling price yields a

300 profit. The profit is then divided by the total cost (

300 / $500) to find the 60% profit.

Step-by-Step Solution

1

Calculate the total cost of the dining set project.

\$250 + \$80 + \$170 = \$500

The total cost must include the initial purchase price plus any additional expenses incurred before selling the item.

2

Calculate the total profit made on the sale.

\$800 - \$500 = \$300

Profit is the difference between the final selling price and the total cost.

3

Calculate the profit as a percentage of the total cost.

\frac{\$300}{\$500} \times 100 = 60\%

Percentage profit is found by dividing the dollar amount of profit by the original total cost and converting to a percentage.

Key Concept

Calculating profit percentage after accounting for overhead and multi-step production costs.

Estimated Time:1m 15s

Question 38Question →

A delivery driver earns a base pay of $80.00 per day plus$ 3.50 for each package delivered. If the driver delivers 40 packages in one day, what is the driver's total gross pay for that day, in dollars?

Show answer & explanation

Answer: 220

Answer

220

The total gross pay is the sum of the fixed base pay (

80.00) and the variable delivery earnings (40 packages ×

3.50 per package =

140.00), which yields a total of

220.00.

Step-by-Step Solution

1

Calculate earnings from package deliveries

$140.00

The driver earns $3.50 for each of the 40 packages delivered (40 × 3.50).

2

Calculate total gross pay

$220.00

Add the base daily pay (

80.00) to the delivery earnings (

140.00) to find the total amount earned for the day.

Key Concept

Calculating total gross pay using a combination of base pay and piece-rate pay

Estimated Time:45s

Question 39Question →

A service member takes out a personal loan of $\$6,000$ from a credit union to cover emergency travel expenses. The credit union charges an annual simple interest rate of $8\%$ . If the loan is fully repaid in exactly $9$ months, what is the total amount, in dollars, that must be repaid?

Show answer & explanation

Answer: 6360

Answer

6360

The total repayment is found by first calculating the interest using

I = PRT

and then adding it to the principal. The time must be converted to years:

9 \text{ months} = 0.75 \text{ years}

.

I = 6000 \times 0.08 \times 0.75 = 360

. The total amount is

6000 + 360 = 6360

.

Step-by-Step Solution

1

Identify the given parameters and convert time to years.

P = 6000

,

R = 0.08

,

T = 9/12 = 0.75

years

The simple interest formula requires time to be in years when the rate is an annual rate.

2

Calculate the accumulated simple interest.

I = 6000 \times 0.08 \times 0.75 = 360

Interest (

I

) is found by multiplying Principal (

P

), Rate (

R

), and Time (

T

).

3

Calculate the total amount to be repaid.

A = 6000 + 360 = 6360

The total repayment includes both the original principal borrowed and the accumulated interest.

Key Concept

Calculating simple interest for a fractional year and determining the total maturity value of a loan.

Question 40Question →

A mechanic takes out a $\$3,000$ loan to purchase upgraded tools. The loan agreement includes a $4\%$ annual simple interest rate. If the loan is paid off in exactly $3$ years, what is the total amount of interest paid?

Show answer & explanation

Answer: 360

Answer

360

The simple interest formula is

I = P \times R \times T

. By plugging in the principal (

\$3,000

), the decimal interest rate (

0.04

), and the time (

3

years), the calculation is

3000 \times 0.04 \times 3 = 360

. Therefore, the total interest paid is

\$360

.

Step-by-Step Solution

1

Identify the given values from the problem statement.

P = 3000

,

R = 4\%

,

T = 3

years

These are the required variables for the simple interest formula.

2

Convert the percentage rate to a decimal.

R = 0.04

Percentages must be in decimal form to perform calculations.

3

Apply the simple interest formula

I = P \times R \times T

.

I = 3000 \times 0.04 \times 3

This formula calculates the total interest earned or paid over a specific time period.

4

Calculate the final product.

360

Multiplying the principal by the rate gives the interest for one year (

120

), and multiplying by 3 gives the total for three years.

Key Concept

Calculating simple interest over a multi-year period.

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes