All practice questions

Question 241Question →

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 242Question →

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.

Question 243Question →

A combat engineering team is tasked with excavating a defensive trench that will be $15 \frac{3}{4}$ miles long. If the team can excavate $2 \frac{1}{3}$ miles of trench per week, how many weeks will it take them to complete the entire project?

6 \frac{3}{4}

36 \frac{3}{4}

9 \frac{3}{4}

13 \frac{5}{12}

Show answer & explanation

Answer: $6 \frac{3}{4}$

Answer

It will take

6 \frac{3}{4}

weeks to complete the trench.

To determine the total time needed to complete a project when given the total amount of work and the rate of work per unit of time, divide the total work by the rate. Converting

15 \frac{3}{4}

and

2 \frac{1}{3}

to improper fractions gives

\frac{63}{4}

and

\frac{7}{3}

. Dividing these fractions (by multiplying by the reciprocal) yields

\frac{63}{4} \times \frac{3}{7} = \frac{27}{4}

, which simplifies to

6 \frac{3}{4}

.

Step-by-Step Solution

1

Identify the total length of the trench and the rate of excavation.

Total length =

15 \frac{3}{4}

miles. Rate =

2 \frac{1}{3}

miles per week.

Understanding the given values is the first step in setting up the correct mathematical operation.

2

Determine the necessary operation to find the total time.

Time = Total Distance

\div

Rate.

When a total amount is being completed at a specific rate per time unit, division is used to find the total time required.

3

Convert the mixed numbers into improper fractions.

15 \frac{3}{4} = \frac{15 \times 4 + 3}{4} = \frac{63}{4}

. And

2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}

.

Fraction division requires improper fractions rather than mixed numbers.

4

Set up and perform the division by multiplying by the reciprocal.

\frac{63}{4} \div \frac{7}{3} = \frac{63}{4} \times \frac{3}{7}

.

Dividing by a fraction is equivalent to multiplying by its reciprocal (inverting the second fraction).

5

Simplify the expression and multiply.

Cross-canceling

63

and

7

leaves

9

and

1

. The equation becomes

\frac{9}{4} \times \frac{3}{1} = \frac{27}{4}

.

Simplifying before multiplying reduces the chance of calculation errors and results in smaller numbers.

6

Convert the improper fraction back to a mixed number.

\frac{27}{4} = 6 \frac{3}{4}

weeks.

The original context and answer choices are presented in mixed numbers.

Key Concept

Dividing mixed numbers in rate problems by converting to improper fractions and multiplying by the reciprocal.

Question 244Question →

A logistics specialist takes out a short-term loan of $\$3,500$ to cover moving expenses. The loan agreement specifies an annual simple interest rate of $6\%$ . If the specialist pays off the entire loan in exactly $8$ months, what is the total amount repaid?

\$3,640

\$3,710

\$4,900

\$5,180

Show answer & explanation

Answer: $\$3,640$

Answer

The total amount repaid is

\$3,640

.

The correct answer accurately calculates the interest for an 8-month period by converting 8 months to 2/3 of a year. Multiplying the principal (

\$3,500

) by the rate (

0.06

) and the time (

2/3

) yields

\$140

in interest. Adding this to the original principal gives the final repayment amount of

\$3,640

.

Step-by-Step Solution

1

Identify the given variables and convert the time period into years.

Principal (

P

) =

\$3,500

, Rate (

R

) =

6\%

or

0.06

, Time (

T

) =

8

months =

\frac{8}{12}

or

\frac{2}{3}

years.

Simple interest formulas require the time variable to be expressed in years when dealing with an annual interest rate.

2

Calculate the simple interest using the formula

I = P \times R \times T

.

I = 3500 \times 0.06 \times \frac{2}{3} = 210 \times \frac{2}{3} = 140

. The interest earned is

\$140

.

This determines the exact cost of borrowing the money for the specified fraction of a year.

3

Add the calculated interest to the original principal to find the total amount to be repaid.

Total Amount (

A

) =

3500 + 140 = 3640

.

The total repayment must include both the borrowed amount (principal) and the accumulated interest.

Key Concept

Calculating Total Repayment with Fractional Year Simple Interest

Question 245Question →

A freelance illustrator earns a fixed weekly retainer of $\$400$ and receives a $10\%$ commission on any artwork sold in galleries. If the illustrator sells $\$1,500$ worth of artwork during the week, what is their total gross pay for that week?

\$150

\$550

\$1,650

\$1,900

Show answer & explanation

Answer: $\$550$

Answer

The total gross pay is

\$550

.

To find the total gross pay, first calculate 10% of the

\$1,500

in sales, which is

\$150

. Then, add this commission amount to the

\$400

fixed retainer, resulting in a total gross pay of

\$550

.

Step-by-Step Solution

1

Calculate the commission earned from the artwork sales.

\$1,500 \times 0.10 = \$150

The illustrator earns a 10% commission on the total value of artwork sold.

2

Add the earned commission to the fixed weekly retainer to find the total gross pay.

\$400 + \$150 = \$550

The total gross pay is the sum of the fixed retainer and any additional commission.

Key Concept

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

Question 246Question →

Match each military vehicle's travel scenario to its correct average unit rate in miles per hour.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The jeep matches to 40 mph, the helicopter to 150 mph, the truck to 55 mph, and the patrol boat to 36 mph.

Each unit rate is found by applying the formula for speed: Speed = Distance ÷ Time. Calculating this for each vehicle yields the correct matching pairs.

Step-by-Step Solution

1

Calculate the unit rate for the jeep.

120 / 3 = 40 miles per hour

To find the average speed, divide total distance by total time.

2

Calculate the unit rate for the helicopter.

300 / 2 = 150 miles per hour

To find the average speed, divide total distance by total time.

3

Calculate the unit rate for the supply truck.

220 / 4 = 55 miles per hour

To find the average speed, divide total distance by total time.

4

Calculate the unit rate for the patrol boat.

180 / 5 = 36 miles per hour

To find the average speed, divide total distance by total time.

Key Concept

A unit rate compares a quantity to one unit of another quantity, often calculated by dividing the total amount by the total time or number of items.

Question 247Question →

A reconnaissance drone squadron currently takes $14\text{ hours}$ to completely map a designated tactical sector when using $6$ identical drones simultaneously. If the task force commander requires the exact same sector to be mapped in $4\text{ hours}$ , how many total drones must be deployed?

Show answer & explanation

Answer: 21

Answer

21

drones

The scenario describes an inverse proportion because increasing the number of active drones decreases the time required to finish the mapping. The total mapping workload is a constant

84

drone-hours (

6\text{ drones} \times 14\text{ hours}

). To complete this exact same workload in a compressed timeframe of

4

hours, a total of

21

drones are needed (

84 \div 4

).

Step-by-Step Solution

1

Identify the relationship between the variables.

The number of drones and the time required are inversely proportional.

Completing a fixed amount of work faster requires proportionally more equipment.

2

Calculate the total amount of work required (the constant of variation).

6\text{ drones} \times 14\text{ hours} = 84\text{ drone-hours}

In an inverse proportion (

x \times y = k

), the product of the two variables remains constant.

3

Calculate the new number of drones required for the target time.

84\text{ drone-hours} \div 4\text{ hours} = 21\text{ drones}

Divide the total work constant by the new required time to solve for the missing variable.

Key Concept

Inverse proportions occur when one variable increases while another decreases such that their product remains constant (

x_1 \times y_1 = x_2 \times y_2

).

Question 248Question →

A manufacturing employee earns a base wage of $\$15.00$ per hour for a standard 40-hour workweek, with time-and-a-half pay for any additional hours worked. In addition to hourly wages, the employee earns a piece-rate bonus for every unit produced that exceeds a weekly quota of 100 units. Last week, the employee worked 48 hours, produced 180 units, and earned a total gross pay of $\$1,060.00$ . What is the piece-rate bonus paid for each unit produced over the quota?

\$2.80

\$3.50

\$4.25

\$7.00

Show answer & explanation

Answer: $\$3.50$

Answer

The piece-rate bonus is

\$3.50

per unit.

The correct piece-rate is found by first isolating the hourly wages. The employee earned

\$600.00

for 40 regular hours and

\$180.00

for 8 overtime hours (at

\$22.50

/hr), totaling

\$780.00

. Subtracting this from the

\$1,060.00

gross pay leaves a

\$280.00

bonus pool. Since the employee produced 80 units above the 100-unit quota, the rate per excess unit is

\$280.00 \div 80 = \$3.50

.

Step-by-Step Solution

1

Calculate the total hourly pay, including standard and overtime hours.

Regular pay:

40 \times \$15.00 = \$600.00

. Overtime pay:

8 \times (\$15.00 \times 1.5) = 8 \times \$22.50 = \$180.00

. Total hourly pay =

\$780.00

.

You must isolate the hourly earnings from the total gross pay to determine how much money came from the piece-rate bonus.

2

Determine the total amount of the piece-rate bonus pool.

\$1,060.00 - \$780.00 = \$280.00

Subtracting the total hourly earnings from the total gross pay gives the exact amount earned purely from assembling extra units.

3

Determine the number of units eligible for the piece-rate bonus.

180 - 100 = 80

units

The bonus is only paid for units produced that exceed the weekly quota of 100.

4

Calculate the bonus amount per excess unit.

\$280.00 \div 80 = \$3.50

Dividing the total bonus pool by the number of eligible units yields the individual piece-rate.

Key Concept

Calculating multi-component compensation by isolating variables (base pay, overtime, and piece-rate quotas).

Question 249Question →

A coastal patrol boat is conducting a surveillance mission. It travels at a steady speed of $12\text{ knots}$ (nautical miles per hour) for $2\text{ hours}$ and $15\text{ minutes}$ . It then increases its speed to $20\text{ knots}$ for $12\text{ minutes}$ to intercept a vessel. What is the total distance traveled by the patrol boat, in nautical miles?

28.2

31

39.2

67

Show answer & explanation

Answer: $31$

Answer

The correct answer is

31

nautical miles.

The total distance is found by calculating the distance for each leg separately. First, convert the times into hours:

15\text{ minutes}

is

0.25\text{ hours}

(making the first leg

2.25\text{ hours}

), and

12\text{ minutes}

is

0.2\text{ hours}

. Multiplying these times by their respective speeds (

12 \times 2.25

and

20 \times 0.2

) gives distances of

27

and

4

nautical miles. Adding these together yields a total of

31

nautical miles.

Step-by-Step Solution

1

Convert the time of the first leg into hours.

2\text{ hours and } 15\text{ minutes} = 2 + \frac{15}{60} = 2.25\text{ hours}

.

Speed is given in knots (nautical miles per hour), so the time must be in hours to cancel the units properly.

2

Calculate the distance traveled during the first leg.

12\text{ knots} \times 2.25\text{ hours} = 27\text{ nautical miles}

.

Using the formula Distance = Rate x Time.

3

Convert the time of the second leg into hours.

12\text{ minutes} = \frac{12}{60} = 0.2\text{ hours}

.

Maintaining consistent units across all calculations.

4

Calculate the distance traveled during the second leg.

20\text{ knots} \times 0.2\text{ hours} = 4\text{ nautical miles}

.

Using the formula Distance = Rate x Time for the second segment.

5

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

27 + 4 = 31\text{ nautical miles}

.

The total distance is the sum of the individual segments of the journey.

Key Concept

Calculating total distance for multi-leg journeys requires converting mixed time units into hours and applying the Distance = Rate x Time formula to each leg separately.

Question 250Question →

A quartermaster unit has a bulk roll of heavy-duty canvas measuring $71 \frac{1}{4}$ yards in length. The unit needs to manufacture custom protective covers for equipment, with each cover requiring exactly $3 \frac{3}{4}$ yards of canvas. How many complete protective covers can the unit manufacture from this roll?

Show answer & explanation

Answer: 19

Answer

19

To find how many items of a specific size can be made from a total amount, you divide the total amount by the size of one item. After converting the mixed numbers to improper fractions (

71 \frac{1}{4} = \frac{285}{4}

and

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

), you multiply

\frac{285}{4}

by the reciprocal

\frac{4}{15}

. The denominators and numerators simplify to yield exactly 19.

Step-by-Step Solution

1

Determine the required mathematical operation.

Division: Total canvas length ÷ Length per cover.

You are distributing a total quantity into equal-sized portions.

2

Convert the mixed numbers into improper fractions.

71 \frac{1}{4} = \frac{285}{4}

and

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

.

Fraction multiplication and division require working with proper or improper fractions rather than mixed numbers.

3

Multiply the first fraction by the reciprocal of the second fraction.

\frac{285}{4} \times \frac{4}{15}

.

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.

4

Simplify the expression and calculate the final quotient.

The 4s cancel, leaving

\frac{285}{15} = 19

.

Cross-simplifying makes the calculation much more manageable without needing a calculator.

Key Concept

Dividing mixed numbers in applied word problems

Question 251Question →

During a materials stress test, a structural beam successfully supported $125\%$ of its rated maximum load before showing signs of fatigue. Which of the following fractions represents this percentage in its simplest form?

\frac{5}{4}

\frac{4}{5}

\frac{1}{8}

\frac{1}{4}

Show answer & explanation

Answer: $\frac{5}{4}$

Answer

The correct fraction in simplest form is

\frac{5}{4}

.

To convert a percentage to a fraction, divide the percentage value by 100. This gives

\frac{125}{100}

. Simplifying this fraction by dividing both the numerator and denominator by their greatest common factor, 25, results in the improper fraction

\frac{5}{4}

.

Step-by-Step Solution

1

Convert the given percentage into a fraction by placing the value over 100.

\frac{125}{100}

A percentage inherently represents a part out of 100.

2

Find the greatest common factor (GCF) for the numerator and denominator to simplify the fraction.

The GCF of 125 and 100 is 25.

Fractions must be expressed in their simplest form to match the standard answer choices.

3

Divide both the numerator and the denominator by 25.

\frac{125 \div 25}{100 \div 25} = \frac{5}{4}

Dividing the top and bottom by the same number scales the fraction down while maintaining its equivalent value.

Key Concept

Converting Percentages Greater Than 100% to Improper Fractions

Question 252Question →

An electronics refurbisher buys a lot of $5$ broken laptops for $\$300$ . The refurbisher spends an additional $\$150$ on replacement parts and $\$50$ on shipping. If the refurbisher wants to make a $40\%$ profit on the total investment, what must be the average selling price of each laptop?

\$84

\$124

\$140

\$700

Show answer & explanation

Answer: $\$140$

Answer

The correct selling price is

\$140

per laptop.

The total investment is the sum of all costs:

\$300

for the broken laptops,

\$150

for replacement parts, and

\$50

for shipping, which equals a total of

\$500

. To make a

40\%

profit on the investment, the refurbisher needs to generate

140\%

of the total cost in revenue (

1.40 \times \$500 = \$700

). Dividing the

\$700

total target revenue by the

5

laptops gives an average selling price of

\$140

per laptop.

Step-by-Step Solution

1

Calculate the total cost (investment).

\$300 + \$150 + \$50 = \$500

To find the total amount invested before calculating the desired profit.

2

Calculate the total revenue needed for a

40\%

profit.

\$500 \times 1.40 = \$700

To determine the total amount of money required to cover all costs and achieve the 40% profit margin.

3

Calculate the average selling price per laptop.

\$700 \div 5 = \$140

To distribute the total required revenue evenly across the 5 laptops.

Key Concept

Calculating net profit by determining total investment, applying a percentage markup, and finding unit price.

Estimated Time:1m 15s

Question 253Question →

For the linear inequality $-\frac{3}{4}(8x - 12) + 2x > -3(x - 4) - 2x$ , the value $x = 3$ is included in the solution set.

True

False

Show answer & explanation

Answer: False

Answer

False, because the solution set is

x > 3

, which strictly excludes the boundary value of 3.

Simplifying both sides of the inequality yields

-4x + 9 > -5x + 12

. Isolating

x

provides the solution set

x > 3

. Because the inequality is strictly 'greater than', it does not include the boundary value of 3, making the statement false.

Step-by-Step Solution

1

Distribute the negative fraction

-\frac{3}{4}

on the left side of the inequality.

-\frac{3}{4}(8x) - (-\frac{3}{4})(12) + 2x = -6x + 9 + 2x

To clear the parentheses and prepare the left side for combining like terms.

2

Distribute the negative integer

-3

on the right side of the inequality.

-3(x) - (-3)(4) - 2x = -3x + 12 - 2x

To clear the parentheses on the right side of the inequality.

3

Combine the like

x

terms on both sides of the inequality.

Left side:

-6x + 2x + 9 = -4x + 9

. Right side:

-3x - 2x + 12 = -5x + 12

. The simplified inequality is

-4x + 9 > -5x + 12

.

To simplify the expression before isolating the variable.

4

Isolate the variable

x

by adding

5x

and subtracting

9

on both sides.

-4x + 5x > 12 - 9

, which simplifies to

x > 3

.

To determine the final solution set for the inequality.

5

Evaluate whether

x = 3

satisfies the solution set

x > 3

.

Since

3

is not greater than

3

, the value is not included in the solution set.

To definitively determine if the original statement is true or false.

Key Concept

Solving multi-step linear inequalities and determining boundary value inclusion

Question 254Question →

A homeowner finances a new refrigerator using a $\$1,200$ store credit plan. The plan charges an annual simple interest rate of $5\%$ . If the homeowner pays off the balance in exactly $2$ years without any prior payments, what is the total amount of interest paid, in dollars?

Show answer & explanation

Answer: 120

Answer

120

The total interest is found by multiplying the principal amount by the annual interest rate and the time in years. Using the formula

I = P \times R \times T

, the calculation is

1200 \times 0.05 \times 2

, which equals $120.

Step-by-Step Solution

1

Identify the given values for principal, rate, and time.

Principal

P = 1200

, Rate

R = 5\% = 0.05

, Time

T = 2

years.

These are the necessary variables for the simple interest formula.

2

Apply the simple interest formula.

I = 1200 \times 0.05 \times 2

The formula for simple interest is

I = P \times R \times T

.

3

Calculate the final product.

I = 120

Multiplying the values determines the total interest paid over the

2

-year period.

Key Concept

Calculating simple interest using the formula

I = P \times R \times T

Question 255Question →

A customer deposits $\$3,000$ into a savings account that pays an annual simple interest rate of $6\%$ . If no additional deposits or withdrawals are made, how much total interest will the account earn after $2$ years?

\$36

\$180

\$360

\$3,600

Show answer & explanation

Answer: \$360

Answer

The account will earn

\$360

in total interest.

The formula for simple interest is

I = P \times R \times T

, where

P

is the principal,

R

is the annual interest rate as a decimal, and

T

is the time in years. Substituting the given values:

I = \$3,000 \times 0.06 \times 2 = \$360

.

Step-by-Step Solution

1

Identify the given values for principal, rate, and time.

P = \$3,000

,

R = 6\% = 0.06

,

T = 2

years.

These are the necessary components for the simple interest formula.

2

Apply the simple interest formula

I = P \times R \times T

.

I = \$3,000 \times 0.06 \times 2

This formula calculates the total interest earned over the given time period.

3

Multiply the values to find the total interest.

I = \$360

This provides the final amount of interest earned.

Key Concept

Simple Interest

Question 256Question →

Determine the missing interest rate and the final maturity value. Fill in the blanks with the correct numeric values.

Fill in the blanks below

A municipal worker invests

\\

5,000$ into a fixed-rate savings certificate. The certificate pays an annual simple interest rate of

\\%

. After

4

years, the certificate has earned

\\

750

in interest, bringing the total maturity value to

\\$$.

Show answer & explanation

Answer

The annual simple interest rate is 3.75% and the total maturity value is $5,750.

The missing interest rate is found by rearranging the formula

I = PRT

to solve for rate:

R = \frac{I}{PT}

. Dividing the interest (

\$750

) by the product of the principal (

\$5,000

) and the time (

4

years) gives a decimal of

0.0375

, which is

3.75\\%

. The total maturity value is simply the initial principal (

\$5,000

) plus the interest earned (

\$750

), which equals

\\

5,750$.

Step-by-Step Solution

1

Identify the given values for the simple interest formula.

Principal (

P

) =

\\

5,000

, Interest (

I

) =

\\

750

, Time (

T

) =

4

years.

To find the missing annual interest rate, we must first list the known values for the formula

I = PRT

.

2

Substitute the known values into the simple interest formula and solve for the rate (

R

).

750 = 5000 \times R \times 4 \Rightarrow 750 = 20000 \times R \Rightarrow R = \frac{750}{20000} = 0.0375

. Converting this decimal to a percentage gives

3.75\\%

.

Isolating

R

allows us to determine the annual percentage rate required to earn the specified interest.

3

Calculate the total maturity value (

A

) by adding the interest earned to the original principal.

A = P + I \Rightarrow A = 5000 + 750 = 5750

.

The total balance at maturity is the sum of the initial investment and the accumulated interest.

Key Concept

Simple Interest Applications

Question 257Question →

A call center representative earns a base salary of $\$400$ per week, plus a $\$5$ bonus for every new customer account they open. If the representative opens $15$ new accounts in one week, what is their total gross pay for that week?

Fill in the blanks below

Total gross pay: $\$

Show answer & explanation

Answer

475

To find the total gross pay, you must first calculate the total bonus earned by multiplying the number of new accounts (

15

) by the bonus per account (

\$5

). This gives a total bonus of

\$75

. You then add this bonus to the base weekly salary of

\$400

, which results in a total gross pay of

\$475

.

Step-by-Step Solution

1

Calculate the total bonus earned from opening new accounts.

\$5 \times 15 = \$75

The representative earns a fixed bonus of

\$5

for each of the

15

accounts opened.

2

Add the total bonus to the weekly base salary to find the total gross pay.

\$400 + \$75 = \$475

Total gross pay is the sum of the guaranteed base salary and any additional bonuses earned during the week.

Key Concept

Calculating total gross pay by combining a fixed base salary with piecework or bonus earnings.

Question 258Question →

A restaurant manager wants to purchase a commercial refrigerator with a list price of $\$3,200$ . Supplier A offers a single discount of $38\%$ off the list price. Supplier B offers a $25\%$ discount off the list price, followed by an additional $15\%$ discount applied to the newly reduced price.

How many dollars does the manager save by choosing the supplier with the lower final price instead of the other supplier?

Show answer & explanation

Answer: 56

Answer

56

Supplier A's final price is

\$1,984

(after a

38\%

reduction from

\$3,200

). Supplier B's final price is

\$2,040

(after a

25\%

reduction to

\$2,400

, followed by a

15\%

reduction). Choosing Supplier A over Supplier B saves the manager

\$2,040 - \$1,984 = \$56

.

Step-by-Step Solution

1

Calculate Supplier A's final sale price.

\$1,984

Supplier A offers a single

38\%

discount.

100\% - 38\% = 62\%

.

0.62 \times \$3,200 = \$1,984

.

2

Calculate Supplier B's price after the initial discount.

\$2,400

Supplier B offers an initial

25\%

discount.

100\% - 25\% = 75\%

.

0.75 \times \$3,200 = \$2,400

.

3

Calculate Supplier B's final sale price.

\$2,040

Supplier B offers an additional

15\%

off the reduced price.

100\% - 15\% = 85\%

.

0.85 \times \$2,400 = \$2,040

.

4

Find the difference between the two final prices.

\$56

Subtracting Supplier A's price from Supplier B's price gives the total savings:

\$2,040 - \$1,984 = \$56

.

Key Concept

Calculating successive discounts and comparing final sale prices.

Question 259Question →

A landscape architect is preparing a design layout for a new rectangular community garden. On the layout, the garden measures $2.5\text{ inches}$ in width and $5\text{ inches}$ in length. The drawing uses a scale where $\frac{1}{4}\text{ inch}$ represents $3\text{ feet}$ . What is the actual area of the community garden in square feet?

112.5

150

180

1,800

Show answer & explanation

Answer: $1,800$

Answer

The actual area of the community garden is

1,800

square feet.

The correct answer is found by first establishing how many feet each inch on the layout represents. Since a quarter of an inch represents 3 feet, one full inch represents 12 feet (4 times 3). Multiplying the layout dimensions by 12 provides the actual dimensions: a width of 30 feet and a length of 60 feet. Finally, multiplying the actual width by the actual length (30 x 60) gives the true area of 1,800 square feet.

Step-by-Step Solution

1

Determine the unit scale factor for 1 inch.

Since

1/4\text{ inch} = 3\text{ feet}

, multiplying both sides by 4 gives

1\text{ inch} = 12\text{ feet}

.

Converting the scale to a 'per inch' rate makes it easier to apply to the drawing measurements.

2

Calculate the actual width and length of the garden.

Actual width =

2.5 \times 12 = 30\text{ feet}

. Actual length =

5 \times 12 = 60\text{ feet}

.

Applying the linear scale factor converts the map dimensions directly into real-world dimensions.

3

Calculate the area of the actual garden.

Area =

30\text{ feet} \times 60\text{ feet} = 1,800\text{ square feet}

.

The area of a rectangle is found by multiplying its length by its width.

Key Concept

Scale Drawings and Area Calculation

Question 260Question →

A commercial diver earns a base rate of $\$45.00$ per hour for the first $40$ hours worked in a week, time-and-a-half for the next $10$ hours (hours $41$ through $50$ ), and double time for any hours worked beyond $50$ hours. Additionally, the diver receives a $\$125$ hazard bonus for each dive exceeding a depth of $100$ feet. Last week, the diver logged a total of $54$ hours of work and completed $3$ dives that exceeded $100$ feet in depth. Based on this information, calculate the diver's total gross pay for the week.

Fill in the blanks below

The diver's total gross pay for the week is

\$

.

Show answer & explanation

Answer

The total gross pay is

\$3,210

.

The correct answer accurately divides the 54 total hours into three distinct pay tiers: 40 hours at the base rate (

\$1,800

), 10 hours at 1.5x (

\$675

), and 4 hours at 2x (

\$360

). It then correctly adds the flat hazard bonus of

\$375

(

3 \times \$125

) to reach the final gross pay of

\$3,210

.

Step-by-Step Solution

1

Calculate the standard pay for the first 40 hours.

\$1,800

\$45.00 \times 40 = \$1,800

2

Calculate the time-and-a-half pay for the next 10 hours.

\$675

The time-and-a-half rate is

\$45.00 \times 1.5 = \$67.50

. For 10 hours, this is

\$67.50 \times 10 = \$675

.

3

Calculate the double time pay for the remaining hours over 50.

\$360

The diver worked 54 total hours, so 4 hours are paid at double time. The rate is

\$45.00 \times 2 = \$90.00

. For 4 hours, this is

\$90.00 \times 4 = \$360

.

4

Calculate the total hazard bonuses earned.

\$375

The diver completed 3 deep dives at

\$125

each.

3 \times \$125 = \$375

.

5

Sum all compensation components to find the total gross pay.

\$3,210

\$1,800 + \$675 + \$360 + \$375 = \$3,210

Key Concept

Calculating multi-tiered compensation involving standard wages, multiple overtime multipliers, and piecework bonuses.

Estimated Time:2m 0s

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

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