Tüm alıştırma soruları

Soru 261Soru →

A furniture store salesperson earns a weekly base salary of $\$500$ , plus a $4\%$ commission on all sales. If the salesperson sells $\$3,000$ worth of furniture in a week, what is their total gross pay for that week?

\$120

\$520

\$620

\$1,700

Cevabı ve açıklamayı göster

Cevap: $\$620$

Cevap

\$620

To find the total gross pay, you must first determine the commission earned by multiplying the total sales by the commission rate.

4\%

of

\$3,000

is

\$120

. Next, add this commission to the base salary.

\$500 + \$120 = \$620

. Therefore, the salesperson's total gross pay is

\$620

.

Adım Adım Çözüm

1

Calculate the commission earned from the sales.

\$3,000 \times 0.04 = \$120

The salesperson earns a 4% commission on their total sales volume.

2

Add the commission to the base salary to find the total gross pay.

\$500 + \$120 = \$620

Total gross pay is the sum of the fixed base salary and the variable commission.

Anahtar Kavram

Calculating total earnings by combining a fixed base salary with a percentage-based commission on sales.

Soru 262Soru →

A civilian contractor works $5$ days a week for $8$ hours each day on a military base. If the contractor earns $\$840$ for the entire week, what is the contractor's hourly wage?

\$21

\$105

\$168

\$210

Cevabı ve açıklamayı göster

Cevap: \$21

Cevap

The contractor's hourly wage is

\$21

.

The total number of hours worked in the week is found by multiplying the

5

days by

8

hours per day, which equals

40

hours. The hourly wage is then calculated by dividing the total weekly earnings by the total hours worked:

\$840 \div 40 = \$21

per hour.

Adım Adım Çözüm

1

Calculate the total number of hours the contractor works in the week.

5 \text{ days} \times 8 \text{ hours/day} = 40 \text{ hours}

To find the hourly wage, the total earnings must be divided by the total hours worked.

2

Divide the total weekly earnings by the total hours worked to find the hourly wage.

\$840 \div 40 \text{ hours} = \$21 \text{ per hour}

The unit rate (hourly wage) is the ratio of total pay to total time.

Anahtar Kavram

Calculating a unit rate by determining the total quantity (hours) and dividing the total amount (earnings) by that quantity.

Soru 263Soru →

A supply clerk notes that $\frac{7}{20}$ of the spare parts inventory needs to be restocked. What decimal represents the portion of the inventory that needs restocking?

Cevabı ve açıklamayı göster

Cevap: 0.35

Cevap

0.35

To convert the fraction

\frac{7}{20}

to a decimal, you divide the numerator (7) by the denominator (20), which equals 0.35. Alternatively, you can multiply both the numerator and denominator by 5 to get the equivalent fraction

\frac{35}{100}

, which is easily read as the decimal 0.35.

Adım Adım Çözüm

1

Identify the fraction that needs to be converted.

The fraction is

\frac{7}{20}

.

This fraction represents the portion of the inventory to be restocked.

2

Convert the fraction into an equivalent fraction with a base-10 denominator, such as 100.

\frac{7 \times 5}{20 \times 5} = \frac{35}{100}

Fractions with a denominator of 100 can be easily and directly written as decimals.

3

Write the resulting fraction as a decimal.

0.35

\frac{35}{100}

represents 35 hundredths, which is 0.35 in decimal form.

Anahtar Kavram

Converting Fractions to Decimals

Alternatif Yöntem

You can use long division to divide 7.00 by 20. 20 goes into 70 three times (with a remainder of 10). Bring down a 0 to make 100. 20 goes into 100 five times, resulting in 0.35.

Tahmini Süre:45s

Soru 264Soru →

During a morning commute, a passenger train maintains a constant speed of $48\text{ miles per hour}$ between two city stations. If the non-stop journey takes exactly $15$ minutes, what is the total distance between the two stations?

12\text{ miles}

7.2\text{ miles}

120\text{ miles}

720\text{ miles}

Cevabı ve açıklamayı göster

Cevap: $12\text{ miles}$

Cevap

The distance between the two stations is

12\text{ miles}

.

The correct answer is found by first converting

15

minutes to hours by dividing by

60

, which gives

0.25

hours. Then, multiplying the speed of

48\text{ miles per hour}

by

0.25

hours results in a distance of

12\text{ miles}

.

Adım Adım Çözüm

1

Identify the formula for distance.

Distance = Rate \times Time

This formula connects speed, time, and distance to find the unknown value.

2

Convert the travel time from minutes to hours.

15 \text{ minutes} = \frac{15}{60} \text{ hours} = 0.25 \text{ hours}

The rate is given in miles per hour, so the time must be in hours to cancel out the units correctly.

3

Multiply the rate by the converted time.

48 \times 0.25 = 12

Applying the values to the distance formula yields the total distance in miles.

Anahtar Kavram

Calculating distance by converting time units to match the rate units.

Tahmini Süre:45s

Soru 265Soru →

A hobbyist is building a scale model of a historic steam locomotive using a scale of $1:48$ . If the actual locomotive is $60\text{ feet}$ long, what is the length of the model locomotive in inches?

Cevabı ve açıklamayı göster

Cevap: 15

Cevap

15

To find the length of the scale model, the actual length of the locomotive must first be converted into inches. Since there are

12\text{ inches}

in a foot,

60\text{ feet}

is equal to

720\text{ inches}

. Using the scale ratio of

1:48

, divide the actual length in inches by

48

to find the model's length. Calculating

720 \div 48

yields a model length of

15\text{ inches}

.

Adım Adım Çözüm

1

Convert the actual length of the locomotive from feet to inches.

60 \times 12 = 720\text{ inches}

The question asks for the model length in inches, so it is necessary to match the units before applying the scale factor.

2

Calculate the model length using the

1:48

scale ratio.

720 \div 48 = 15\text{ inches}

The scale

1:48

means the model is

48

times smaller than the actual object.

Anahtar Kavram

Applying scale ratios across different units of measurement.

Soru 266Soru →

Which of the following represents the correct solution set for the inequality below?

4(x - 3) - 3(2x + 5) \geq x - 12

x \leq -5

x \geq -5

x \leq 5

x \geq 5

Cevabı ve açıklamayı göster

Cevap: $x \leq -5$

Cevap

The correct solution is

x \leq -5

.

The correct answer is derived by carefully distributing the values across the parentheses (yielding

4x - 12 - 6x - 15 \geq x - 12

), combining the like terms to form

-2x - 27 \geq x - 12

, and isolating

x

to get

-3x \geq 15

. Crucially, dividing both sides by

-3

requires reversing the direction of the inequality, which correctly results in

x \leq -5

.

Adım Adım Çözüm

1

Distribute the coefficients outside the parentheses into the terms inside.

4x - 12 - 6x - 15 \geq x - 12

This removes the parentheses. Care must be taken to multiply -3 by +5 correctly to get -15.

2

Combine the like terms on the left side of the inequality.

-2x - 27 \geq x - 12

Simplifying both sides makes it easier to isolate the variable.

3

Move all terms containing

x

to one side and all constant terms to the other side.

-3x \geq 15

Subtracting

x

from both sides gives

-3x

, and adding

27

to both sides gives

15

.

4

Divide both sides by -3 and reverse the inequality symbol.

x \leq -5

Whenever you multiply or divide an inequality by a negative number, the direction of the inequality sign must be flipped to maintain a true mathematical statement.

Anahtar Kavram

Solving multi-step linear inequalities involving distribution and the inequality sign flip rule.

Soru 267Soru →

A logistics officer is allocating a stockpile of $112 \frac{1}{2}$ gallons of specialty aviation lubricant. The primary maintenance hangar is allocated $\frac{3}{5}$ of the total stockpile. The remaining lubricant is to be divided equally among $4$ flightline repair vehicles. How many gallons of lubricant will each repair vehicle receive?

11 \frac{1}{4}

16 \frac{7}{8}

180

7 \frac{13}{14}

Cevabı ve açıklamayı göster

Cevap: $11 \frac{1}{4}$

Cevap

The correct answer is

11 \frac{1}{4}

gallons, which is calculated by finding the remaining portion of the stockpile and dividing it equally among the four vehicles.

The correct answer accurately determines that

\frac{2}{5}

of the total stockpile remains, calculates that remaining amount to be

45

gallons, and then correctly divides those

45

gallons equally among the

4

repair vehicles to yield

11 \frac{1}{4}

gallons.

Adım Adım Çözüm

1

Determine the fraction of the stockpile that remains for the repair vehicles.

1 - \frac{3}{5} = \frac{2}{5}

The primary hangar is allocated

\frac{3}{5}

of the total, meaning the rest is left for the vehicles.

2

Calculate the volume of the remaining lubricant.

\frac{2}{5} \times 112 \frac{1}{2} = \frac{2}{5} \times \frac{225}{2} = \frac{450}{10} = 45

gallons.

Multiplying the remaining fraction by the total initial volume gives the exact gallons available.

3

Divide the remaining volume equally among the 4 repair vehicles.

45 \div 4 = \frac{45}{4} = 11 \frac{1}{4}

gallons.

The total remaining amount must be distributed evenly to determine each vehicle's individual share.

Anahtar Kavram

Fraction Multiplication and Division in Context

Soru 268Soru →

A woodworker is purchasing a bulk supply of lumber with a regular total price of $\$800$ . The supplier offers two different discount options for the purchase:

Option 1: A $\$150$ instant rebate on the regular price, followed by a $15\%$ discount on the remaining balance.
Option 2: A $25\%$ discount on the regular price, followed by an additional $5\%$ discount on the reduced price.

What is the positive difference in the final sale price between the two options?

\$17.50

\$7.50

\$135.00

\$44.50

Cevabı ve açıklamayı göster

Cevap: $\$17.50$

Cevap

The correct difference between the two options is

\$17.50

.

Option 1 evaluates to

\$552.50

by first subtracting the

\$150

rebate and then taking

15\%

off the remaining

\$650

. Option 2 evaluates to

\$570.00

by first taking

25\%

off the original

\$800

, yielding

\$600

, and then taking an additional

5\%

off the

\$600

, which is

\$30

. The difference between

\$570.00

and

\$552.50

is

\$17.50

.

Adım Adım Çözüm

1

Calculate the price for Option 1 after the instant rebate.

\$800 - \$150 = \$650

The rebate is a flat amount subtracted from the initial regular price before any percentage discounts are applied.

2

Calculate the final price for Option 1 after the 15% discount.

\$650 - (\$650 \times 0.15) = \$650 - \$97.50 = \$552.50

The

15\%

discount applies to the remaining balance of

\$650

.

3

Calculate the price for Option 2 after the initial 25% discount.

\$800 - (\$800 \times 0.25) = \$800 - \$200 = \$600

The first discount is applied directly to the regular price.

4

Calculate the final price for Option 2 after the additional 5% discount.

\$600 - (\$600 \times 0.05) = \$600 - \$30 = \$570.00

Successive discounts are applied to the newly reduced price, not the original price.

5

Calculate the positive difference between the two final prices.

\$570.00 - \$552.50 = \$17.50

Subtracting the smaller final price from the larger final price provides the difference.

Anahtar Kavram

Calculating successive discounts, rebates, and comparing multiple-step financial scenarios.

Soru 269Soru →

A warehouse forklift moves $84$ cargo pallets in $6$ hours. At this constant rate, how many pallets does the forklift move per hour?

Cevabı ve açıklamayı göster

Cevap: 14

Cevap

The forklift moves

14

pallets per hour.

To determine the unit rate, divide the total quantity (

84

pallets) by the total elapsed time (

6

hours). The result is a constant rate of

14

pallets per hour.

Adım Adım Çözüm

1

Identify the total quantity of items and the total time.

Total pallets =

84

, Total time =

6

hours.

These are the two values needed to set up the unit rate calculation.

2

Divide the total pallets by the total hours.

84 \div 6 = 14

The unit rate 'pallets per hour' requires dividing the number of pallets by the number of hours.

Anahtar Kavram

Calculating unit rates

Tahmini Süre:45s

Soru 270Soru →

A recruitment office processes $400$ applications in a month. If $15\%$ of the applicants meet the requirements for a specialized technical role, how many applicants qualify for this role?

6

60

340

385

Cevabı ve açıklamayı göster

Cevap: $60$

Cevap

Exactly

60

applicants qualify for the role.

To calculate

15\%

of

400

, first convert the percentage to its decimal form, which is

0.15

. Then, multiply the total number of applicants (

400

) by the decimal (

0.15

). The calculation

400 \times 0.15

equals

60

. Therefore,

60

applicants meet the requirements.

Adım Adım Çözüm

1

Convert the percentage to a decimal.

15\% = 0.15

A percentage must be expressed as a decimal or fraction to be used in a calculation.

2

Multiply the total number of applications by the decimal.

400 \times 0.15 = 60

Multiplying the total quantity by the percentage rate gives the fractional amount representing that percentage.

Anahtar Kavram

To find a specific percentage of a quantity, convert the percent to a decimal (or fraction) and multiply it by the total amount.

Tahmini Süre:45s

Soru 271Soru →

Read the scenario and fill in the missing numerical values for the discount and the sale price.

Aşağıdaki boşlukları doldurun

A hardware store is selling a power drill with a regular price of

\$120

. If the store is offering a

20\%

discount on all power tools, calculate the savings and the new price.

Discount amount:

\$

Final sale price:

\$

Cevabı ve açıklamayı göster

Cevap

The discount amount is

\$24

, and the final sale price is

\$96

.

To find the discount amount, multiply the regular price (

\$120

) by the discount percentage (

20\%

or

0.20

), which equals

\$24

. To find the final sale price, subtract the

\$24

discount from the

\$120

regular price, which equals

\$96

.

Adım Adım Çözüm

1

Convert the discount percentage to a decimal.

20\% = 0.20

Percentages must be in decimal form to multiply them by dollar amounts.

2

Calculate the discount amount by multiplying the original price by the decimal discount rate.

\$120 \times 0.20 = \$24

This determines the exact dollar amount that will be saved.

3

Subtract the discount amount from the original price to find the final sale price.

\$120 - \$24 = \$96

The final sale price is the original price minus the savings.

Anahtar Kavram

Calculating the dollar amount of a percentage discount and determining the final sale price.

Tahmini Süre:1m 0s

Soru 272Soru →

An individual borrows $\$4,000$ to purchase a used motorcycle. The loan has an annual simple interest rate of $7\%$ . If the loan is paid off in exactly $24$ months, how much total interest will the borrower pay?

\$280

\$560

\$5,600

\$6,720

Cevabı ve açıklamayı göster

Cevap: $\$560$

Cevap

The total interest paid is

\$560

.

The correct answer accurately uses the simple interest formula

I = P \times R \times T

. The principal (

P

) is

\$4,000

, the rate (

R

) is

0.07

, and the time (

T

) in years is

2

(since

24

months equals

2

years). Multiplying these together yields

\$4,000 \times 0.07 \times 2 = \$560

.

Adım Adım Çözüm

1

Identify the principal amount (

P

), annual interest rate (

R

), and time (

T

) given in the problem.

P = \$4,000

,

R = 7\%

, and

T = 24

months.

These are the required variables for the simple interest formula.

2

Convert the interest rate from a percentage to a decimal.

7\% = 0.07

Mathematical formulas require percentages to be in decimal form.

3

Convert the time duration from months to years to match the annual interest rate.

24 \text{ months} \div 12 \text{ months/year} = 2 \text{ years}

.

The interest rate is annual, so the time must also be in years.

4

Apply the simple interest formula,

I = P \times R \times T

.

I = \$4,000 \times 0.07 \times 2 = \$560

.

This calculates the total interest accrued over the 2-year period.

Anahtar Kavram

Simple Interest Calculation with Time Conversion

Soru 273Soru →

A marketing consultant earns a weekly base salary of $\$850$ . She also earns a $4\%$ commission on any client contracts she secures beyond a weekly quota of $\$5,000$ . If she secures $\$18,500$ in contracts this week, what are her total gross earnings?

\$540

\$904

\$1,390

\$1,590

Cevabı ve açıklamayı göster

Cevap: \$1,390

Cevap

\$1,390

The correct answer is found by subtracting the

\$5,000

quota from the total

\$18,500

in contracts to find the commissionable amount (

\$13,500

). Then, calculating

4\%

of that amount yields

\$540

in commission. Finally, adding the

\$540

commission to the

\$850

base salary results in total gross earnings of

\$1,390

.

Adım Adım Çözüm

1

Determine the amount of sales eligible for commission.

\$18,500 - \$5,000 = \$13,500

The consultant only earns commission on contracts beyond the

\$5,000

quota.

2

Calculate the commission earned on the eligible sales.

0.04 \times \$13,500 = \$540

The commission rate is

4\%

, which is

0.04

as a decimal.

3

Add the commission to the base salary to find total gross earnings.

\$850 + \$540 = \$1,390

Total earnings are the sum of the fixed base salary and the variable commission.

Anahtar Kavram

Calculating gross pay involving a base salary and a tiered commission structure.

Tahmini Süre:1m 15s

Soru 274Soru →

A freight train departs from a central hub to deliver materials across two different transit zones. In the primary zone, the train maintains a constant speed of $60\text{ mph}$ for $2\text{ hours and } 45\text{ minutes}$ . Upon entering the secondary zone, it reduces its speed to $40\text{ mph}$ for the remaining $1\text{ hour and } 15\text{ minutes}$ of the route. What is the total distance traveled by the freight train?

215\text{ miles}

200\text{ miles}

193\text{ miles}

165\text{ miles}

Cevabı ve açıklamayı göster

Cevap: $215\text{ miles}$

Cevap

The freight train traveled a total distance of

215\text{ miles}

.

To find the total distance, each segment must be calculated separately using the formula

\text{Distance} = \text{Speed} \times \text{Time}

. For the primary zone,

2\text{ hours and } 45\text{ minutes}

is

2.75\text{ hours}

. Multiplying

60\text{ mph}

by

2.75\text{ hours}

yields

165\text{ miles}

. For the secondary zone,

1\text{ hour and } 15\text{ minutes}

is

1.25\text{ hours}

. Multiplying

40\text{ mph}

by

1.25\text{ hours}

yields

50\text{ miles}

. The total distance is the sum of these two segments:

165 + 50 = 215\text{ miles}

.

Adım Adım Çözüm

1

Convert the travel time for the primary zone into hours.

2\text{ hours and } 45\text{ minutes} = 2 + \frac{45}{60} = 2.75\text{ hours}

.

Speed is given in miles per hour (mph), so time must be in hours to calculate distance.

2

Calculate the distance traveled in the primary zone.

\text{Distance} = \text{Speed} \times \text{Time} = 60\text{ mph} \times 2.75\text{ hours} = 165\text{ miles}

.

Applying the standard distance formula for the first segment.

3

Convert the travel time for the secondary zone into hours.

1\text{ hour and } 15\text{ minutes} = 1 + \frac{15}{60} = 1.25\text{ hours}

.

Time must be consistently in hours to match the speed unit.

4

Calculate the distance traveled in the secondary zone.

\text{Distance} = 40\text{ mph} \times 1.25\text{ hours} = 50\text{ miles}

.

Applying the distance formula for the second segment.

5

Add the distances of both zones to find the total distance.

165\text{ miles} + 50\text{ miles} = 215\text{ miles}

.

The total distance is the sum of all individual legs of the journey.

Anahtar Kavram

Calculating distance across multiple segments requires converting time into consistent units (hours) before applying the distance formula (

d = rt

) to each segment and summing the results.

Soru 275Soru →

An electronics salesperson earns a base weekly salary of $\$650$ plus a $6\%$ commission on their total sales. If they sell $\$4,500$ worth of electronics in one week, what is their total gross pay, in dollars, for that week?

Cevabı ve açıklamayı göster

Cevap: 920

Cevap

920

The total gross pay is the sum of the base salary and the commission earned. The commission is

6\%

of

\$4,500

, which is calculated as

0.06 \times 4500 = 270

. Adding this to the base salary gives

650 + 270 = 920

.

Adım Adım Çözüm

1

Calculate the commission earned from sales.

\$270

The commission is

6\%

of the

\$4,500

in total sales. Multiply

4500

by

0.06

to find this amount.

2

Calculate the total gross pay.

\$920

Add the commission earned (

\$270

) to the base weekly salary (

\$650

) to determine the total earnings for the week.

Anahtar Kavram

Calculating total gross pay by combining a base salary with a percentage commission.

Soru 276Soru →

A craftsman purchases $60$ wooden boards at $\$3.00$ each to build custom storage chests. He spends an additional $\$40.00$ on hinges and pays a $\$20.00$ delivery fee for the materials. If he builds $10$ chests and sells them all for $\$30.00$ each, what is his profit percentage?

20\%

2.5\%

25\%

125\%

Cevabı ve açıklamayı göster

Cevap: $25\%$

Cevap

The profit percentage is

25\%

.

The correct answer is found by first determining the total cost, which includes the materials and all overhead expenses (

\$180 + \$40 + \$20 = \$240

). Next, find the total revenue (

\$30 \times 10 = \$300

). The profit is the difference (

\$300 - \$240 = \$60

). Finally, divide the profit by the total cost to find the percentage:

\$60 / \$240 = 0.25

, which is

25\%

.

Adım Adım Çözüm

1

Calculate the initial cost of the wooden boards.

60 \times \$3.00 = \$180.00

To find the base material cost before adding overhead expenses.

2

Calculate the total cost (investment).

\$180.00 + \$40.00 \text{ (hinges)} + \$20.00 \text{ (delivery)} = \$240.00

All overhead and preparation expenses must be included to find the true total cost.

3

Calculate the total revenue from selling the chests.

10 \times \$30.00 = \$300.00

To determine the total amount earned from sales.

4

Calculate the profit amount.

\$300.00 - \$240.00 = \$60.00

Profit is the difference between total revenue and total cost.

5

Calculate the profit percentage.

(\$60.00 / \$240.00) \times 100 = 0.25 \times 100 = 25\%

Profit percentage is the profit amount divided by the total cost, expressed as a percentage.

Anahtar Kavram

Calculating percentage profit with multi-step overhead costs

Tahmini Süre:1m 15s

Soru 277Soru →

A military supply convoy travels at a steady speed of $40\text{ miles per hour}$ for $2\text{ hours}$ . Then, it travels at a steady speed of $50\text{ miles per hour}$ for $1\text{ hour}$ . What is the total distance traveled by the convoy? Provide your answer including the unit (e.g., '130 miles').

Cevabı ve açıklamayı göster

Cevap: 130 miles; 130 mi; 130

Cevap

130 miles

To find the total distance, you must calculate the distance for each segment separately using the formula Distance = Rate × Time, and then add them together. The first segment covers 80 miles (40 mph × 2 hours) and the second segment covers 50 miles (50 mph × 1 hour), resulting in a total distance of 130 miles.

Adım Adım Çözüm

1

Calculate the distance for the first part of the trip.

40 \times 2 = 80\text{ miles}

Distance is equal to rate multiplied by time.

2

Calculate the distance for the second part of the trip.

50 \times 1 = 50\text{ miles}

Apply the distance formula to the second segment.

3

Add the distances from both parts of the trip to find the total distance.

80 + 50 = 130\text{ miles}

The total distance is the sum of the individual segment distances.

Anahtar Kavram

Calculating total distance for a multi-segment journey by applying the formula Distance = Rate × Time to each segment.

Tahmini Süre:45s

Soru 278Soru →

A military dining facility prepares $800$ meals for a special event. If $45\%$ of these meals are vegetarian, how many vegetarian meals were prepared?

Cevabı ve açıklamayı göster

Cevap: 360

Cevap

360

To find the number of vegetarian meals, multiply the total number of meals (

800

) by the decimal form of the percentage (

0.45

), which yields exactly

360

meals.

Adım Adım Çözüm

1

Convert the percentage to a decimal.

45\% = 0.45

Percentages must be converted to decimals or fractions to perform arithmetic operations.

2

Multiply the total quantity by the decimal.

800 \times 0.45 = 360

To find a percentage of a quantity, multiply the total by the decimal equivalent of the percentage.

Anahtar Kavram

Calculating a percentage of a given whole number

Tahmini Süre:45s

Soru 279Soru →

A civil engineering unit is mixing concrete for a rapid runway repair. The specialized mixture requires a weight ratio of $3$ parts Portland cement to $5$ parts aggregate. If a repair job requires a total of $400$ pounds of this dry mixture, how many pounds of Portland cement are needed?

50

150

240

250

Cevabı ve açıklamayı göster

Cevap: $150$

Cevap

The correct amount is

150

pounds.

The mixture consists of

3

parts cement and

5

parts aggregate, meaning there are

8

parts in total. Since the entire mixture weighs

400

pounds, each part weighs

50

pounds (

400 \div 8

). To find the amount of Portland cement, which represents

3

of those parts, we multiply

50

by

3

to get

150

pounds.

Adım Adım Çözüm

1

Determine the total number of parts in the given ratio.

3 \text{ (cement)} + 5 \text{ (aggregate)} = 8 \text{ total parts}

Because the

400

pounds represents the entire mixture, we need to know the total parts that make up that whole mixture.

2

Calculate the weight of one single part.

400 \div 8 = 50 \text{ pounds per part}

Dividing the total weight by the total number of parts gives the value of a single proportional unit.

3

Calculate the total weight of the Portland cement.

50 \times 3 = 150 \text{ pounds}

The ratio specifies

3

parts of Portland cement, so we multiply the weight of one part by

3

.

Anahtar Kavram

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

Soru 280Soru →

A mess hall crew prepares $240$ field rations in $120$ minutes. What is the crew's constant preparation rate in rations per hour?

2

12

120

480

Cevabı ve açıklamayı göster

Cevap: 120

Cevap

120

The rate is found by first converting

120

minutes into

2

hours, then dividing the

240

rations by

2

hours to obtain

120

rations per hour.

Adım Adım Çözüm

1

Convert the given time from minutes to hours.

120 \text{ minutes} = 2 \text{ hours}

The question asks for the rate in rations per hour, so the time unit must be in hours.

2

Divide the total number of rations by the total time in hours.

240 \div 2 = 120

Dividing the total quantity by the total time calculates the unit rate.

Anahtar Kavram

Calculating a unit rate often requires first converting time into the requested units before performing division.

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