All practice questions

Question 61Question →

A photographer is buying a new camera bag. The original price of the bag is $\$80$ . If the store is having a clearance sale and offers a $25\%$ discount, what is the final sale price of the camera bag in dollars?

Show answer & explanation

Answer: 60

Answer

The final sale price of the camera bag is

\$60

.

To find the final sale price, first calculate the discount amount by multiplying the original price (

\$80

) by the discount rate (

25\%

or

0.25

), which equals

\$20

. Then, subtract this discount from the original price (

\$80 - \$20

) to get the final sale price of

\$60

.

Step-by-Step Solution

1

Calculate the discount amount in dollars.

\$20

The discount is

25\%

of the original price, so we multiply

\$80

by

0.25

.

2

Calculate the final sale price by subtracting the discount from the original price.

\$60

The final sale price is the original price minus the discount savings (

\$80 - \$20

).

Key Concept

Calculating a single-step discount and final sale price.

Question 62Question →

An entrepreneur purchases $5$ used electric scooters for $\$120$ each. She pays an additional flat fee of $\$150$ to replace the batteries for the entire batch. If she sells all $5$ scooters for $\$210$ each, what is her overall profit percentage on this investment?

Show answer & explanation

Answer: 40

Answer

40

The correct answer is found by first calculating the total investment, which includes both the purchase price of the scooters (

600) and the battery replacement costs (

150), yielding a total cost basis of

750. The total revenue from sales is

1,050. Subtracting the total cost from the revenue gives a net profit of

300. Finally, dividing the

300 profit by the $750 total investment yields a profit percentage of 40%.

Step-by-Step Solution

1

Calculate the total cost of purchasing the used scooters.

5 \times \$120 = \$600

This establishes the initial base cost before overhead.

2

Calculate the total investment by adding the battery replacement cost.

\$600 + \$150 = \$750

Profit must be calculated using the total cost basis, including all overhead expenses.

3

Calculate the total revenue from selling the scooters.

5 \times \$210 = \$1,050

Total revenue is needed to find the net profit.

4

Determine the net profit.

\$1,050 - \$750 = \$300

Net profit is total revenue minus total investment.

5

Calculate the profit percentage.

\frac{300}{750} \times 100 = 40\%

Profit percentage is the net profit divided by the total investment (cost basis), expressed as a percentage.

Key Concept

Calculating profit percentage by factoring in both unit costs and multi-step overhead expenses.

Estimated Time:1m 0s

Question 63Question →

A military cargo plane needs to transport supplies to a base that is $900$ miles away. If the plane flies at a constant speed of $300$ miles per hour, how many hours will the flight take?

Show answer & explanation

Answer: 3

Answer

The flight will take 3 hours.

To find the travel time, the total distance must be divided by the constant rate of speed. By applying the formula

\text{Time} = \frac{\text{Distance}}{\text{Rate}}

, dividing the

900

mile distance by the

300

mile per hour speed yields exactly

3

hours.

Step-by-Step Solution

1

Identify the known values from the word problem.

\text{Distance} = 900

miles,

\text{Rate} = 300

miles per hour.

These are the two variables required to solve for the missing variable, which is time.

2

Apply the time formula.

\text{Time} = \frac{900}{300} = 3

.

Time is equal to total distance divided by the constant rate.

Key Concept

Calculating elapsed time using the distance and rate formula.

Estimated Time:45s

Question 64Question →

A combat medic is restocking his medical kit. He purchases $5$ rolls of medical tape for $\$2.45$ each and $3$ bottles of antiseptic for $\$4.20$ each. If he pays with a $\$50.00$ bill and there is no sales tax, what is the exact amount of change he receives?

Show answer & explanation

Answer: 25.15

Answer

25.15

The correct answer is found by calculating the total cost of all items (

\$12.25 + \$12.60 = \$24.85

) and then subtracting that total from the

\$50.00

payment amount to find the change due (

\$50.00 - \$24.85 = \$25.15

).

Step-by-Step Solution

1

Calculate the total cost of the medical tape.

$12.25

Multiply the quantity (5) by the unit price ($2.45).

2

Calculate the total cost of the antiseptic.

$12.60

Multiply the quantity (3) by the unit price ($4.20).

3

Add the costs of the tape and antiseptic to find the total purchase amount.

$24.85

12.25 +

12.60 = $24.85.

4

Subtract the total purchase amount from the payment amount.

$25.15

50.00 -

24.85 = $25.15. This is the exact change received.

Key Concept

Decimal Operations and Currency Word Problems

Question 65Question →

A freight broker earns a weekly base salary of $\$600$ . They also earn a $3\%$ commission on their first $\$10,000$ in freight sales for the week, and a $5\%$ commission on any sales exceeding $\$10,000$ . If the broker secures $\$24,000$ in freight sales this week, what are their total gross earnings for the week in dollars?

Show answer & explanation

Answer: 1600

Answer

1600

The total earnings consist of three parts: the fixed base salary (

600), the 3% commission on the first

10,000 of sales (

300), and the 5% commission on the remaining

14,000 of sales (

700). Adding these amounts together (

600 +

300 +

700) results in total gross earnings of $1,600.

Step-by-Step Solution

1

Calculate the commission earned on the first $10,000 of sales.

$300

The broker earns 3% on the first

10,000.

10,000 \times 0.03 = $300.

2

Calculate the remaining sales volume above the $10,000 threshold.

$14,000

Total sales were

24,000. The amount over

10,000 is

24,000 -

10,000 = $14,000.

3

Calculate the commission earned on the remaining sales.

$700

The broker earns 5% on sales exceeding

10,000.

14,000 \times 0.05 = $700.

4

Calculate total gross earnings.

$1,600

Add the base salary, first-tier commission, and second-tier commission:

600 +

300 +

700 =

1,600.

Key Concept

Calculating total gross earnings involving a base salary and a tiered commission structure.

Estimated Time:1m 30s

Question 66Question →

During a training exercise, a reconnaissance team travels a distance of $18$ miles in exactly $45$ minutes using all-terrain vehicles. What is their average speed in miles per hour?

Show answer & explanation

Answer: 24

Answer

24

To find the average speed in miles per hour, the travel time must first be converted into hours. Since there are

60

minutes in an hour,

45

minutes is equal to

0.75

hours (or

\frac{3}{4}

of an hour). Dividing the distance of

18

miles by the time of

0.75

hours yields a rate of

24

miles per hour.

Step-by-Step Solution

1

Convert the travel time from minutes to hours.

45 \text{ minutes} = \frac{45}{60} \text{ hours} = 0.75 \text{ hours}

(or

\frac{3}{4}

hour).

The speed is requested in miles per hour, so the time must be converted to hours to match the units of the rate.

2

Calculate the average speed using the rate formula

r = \frac{d}{t}

.

r = \frac{18 \text{ miles}}{0.75 \text{ hours}} = 24 \text{ mph}

.

Rate equals total distance divided by total time.

Key Concept

Calculating rate with necessary time unit conversions

Estimated Time:1m 0s

Question 67Question →

A quartermaster is allocating $2,100$ yards of heavy-duty canvas to manufacture temporary shelters, cot covers, and equipment tarps. The canvas is divided among these three projects in a ratio of $6:5:3$ , respectively. What is the difference, in yards, between the amount of canvas allocated for the temporary shelters and the amount allocated for the equipment tarps?

Show answer & explanation

Answer: 450

Answer

450

The correct answer is found by determining that the total ratio consists of 14 parts, meaning each part represents 150 yards (2100 / 14). The difference between the shelters (6 parts) and tarps (3 parts) is 3 parts, which equals 450 yards (3 * 150).

Step-by-Step Solution

1

Calculate the total number of parts in the ratio.

6 + 5 + 3 = 14

total parts.

To divide the total amount of canvas proportionally, we first need to determine the total number of equal parts.

2

Determine the value of a single part.

2,100 \div 14 = 150

yards per part.

Dividing the total yards by the total parts gives the amount of canvas for each ratio unit.

3

Calculate the difference in ratio parts between the shelters and the tarps.

6

parts (shelters) -

3

parts (tarps) =

3

parts difference.

We need the difference between the two allocations. Finding the difference in parts directly is the most efficient method.

4

Calculate the difference in yards.

3 \times 150 = 450

yards.

Multiplying the difference in ratio parts by the value of a single part yields the final answer.

Key Concept

Dividing a total quantity into a given ratio by finding the value of a single part.

Question 68Question →

A land surveyor is measuring a four-sided plot of land. They record three of the interior angles as $78^\circ$ , $104^\circ$ , and $83^\circ$ . What is the measure of the fourth interior angle, in degrees?

Show answer & explanation

Answer: 95

Answer

The fourth interior angle measures

95^\circ

.

The correct answer is found by subtracting the sum of the three known angles (

265^\circ

) from the total interior angle sum of a quadrilateral (

360^\circ

), which yields

95^\circ

.

Step-by-Step Solution

1

Identify the total sum of interior angles for a quadrilateral.

360^\circ

A quadrilateral has 4 sides, and the sum of interior angles is calculated as

(n - 2) \times 180^\circ

. For

n = 4

, this is

2 \times 180^\circ = 360^\circ

.

2

Calculate the sum of the three given angles.

78^\circ + 104^\circ + 83^\circ = 265^\circ

To find the missing part, we must first determine the combined total of the known angles.

3

Subtract the sum of the given angles from the total quadrilateral angle sum.

360^\circ - 265^\circ = 95^\circ

The remaining amount represents the exact measure of the fourth interior angle.

Key Concept

The sum of the interior angles of any convex quadrilateral is always exactly

360^\circ

.

Question 69Question →

A naval supply ship travels $150$ nautical miles in $10$ hours, and then travels an additional $90$ nautical miles in $5$ hours. What is the ship's average speed for the entire trip, in knots (nautical miles per hour)?

Show answer & explanation

Answer: 16

Answer

16 knots

The overall average speed is calculated correctly by finding the total distance (

150 + 90 = 240

nautical miles) and dividing it by the total time (

10 + 5 = 15

hours). This calculation (

240 \div 15

) results in exactly

16

knots.

Step-by-Step Solution

1

Calculate the total distance traveled for the entire trip.

150 + 90 = 240

nautical miles

Finding average speed requires knowing the complete distance covered across all segments of the trip.

2

Calculate the total time taken for the entire trip.

10 + 5 = 15

hours

Finding average speed requires knowing the total elapsed time.

3

Divide the total distance by the total time.

240 \div 15 = 16

knots

The formula for average speed is Total Distance divided by Total Time.

Key Concept

Average speed is calculated by dividing the total distance traveled by the total time taken.

Question 70Question →

A triangular pennant has a base of $8$ inches and a height of $15$ inches. What is the area of the pennant, in square inches?

Show answer & explanation

Answer: 60

Answer

60

The correct area is found by multiplying the base by the height, and then dividing by two according to the standard triangle area formula.

Step-by-Step Solution

1

Identify the formula for the area of a triangle.

A = \frac{1}{2}bh

The object is described as a triangular pennant.

2

Substitute the given base and height into the formula.

A = \frac{1}{2}(8)(15)

The base is given as

8

inches and the height is

15

inches.

3

Calculate the final product.

60

Multiplying the terms:

\frac{1}{2} \times 8 = 4

, and

4 \times 15 = 60

.

Key Concept

Area of a Triangle

Estimated Time:45s

Question 71Question →

The sum of the interior angles of a convex polygon is exactly three times the sum of its exterior angles. How many sides does this polygon have?

Show answer & explanation

Answer: 8

Answer

8

Applying the core polygon properties, the interior angle sum is

180^\circ(n - 2)

and the exterior angle sum is

360^\circ

. Setting

180^\circ(n - 2) = 3(360^\circ)

and solving for

n

yields 8.

Step-by-Step Solution

1

Identify the interior angle sum formula.

Sum =

180^\circ(n - 2)

This formula provides the total sum of all interior angles for an

n

-sided polygon.

2

Identify the exterior angle sum property.

Sum =

360^\circ

A fundamental property of all convex polygons is that the sum of their exterior angles is exactly

360^\circ

.

3

Set up the algebraic equation.

180^\circ(n - 2) = 3 \times 360^\circ

The question states the interior sum is exactly three times the exterior sum.

4

Solve the equation for

n

.

n = 8

Dividing

1080^\circ

by

180^\circ

yields 6, and adding 2 gives a final side count of 8.

Key Concept

Polygon Angle Sum Theorems

Question 72Question →

A machinist earns a regular hourly rate of $\$26.00$ for a standard $40$ -hour workweek. Any hours worked over $40$ in a single week are paid at a time-and-a-half overtime rate. Additionally, working the night shift adds a flat $\$3.50$ per hour differential to their base rate before the overtime multiplier is applied. If the machinist worked $46$ hours last week, and all of those hours were on the night shift, what was their total gross pay in dollars?

Show answer & explanation

Answer: 1445.5

Answer

1445.50

The total gross pay is calculated by first establishing the adjusted base rate for the night shift, which is the regular rate plus the differential:

\$26.00 + \$3.50 = \$29.50

. The machinist worked

40

regular hours at this rate, earning

40 \times \$29.50 = \$1,180.00

. The

6

remaining hours are overtime, paid at

1.5

times the adjusted rate:

\$29.50 \times 1.5 = \$44.25

. Multiplying this by the

6

overtime hours gives

6 \times \$44.25 = \$265.50

. Adding the regular pay and overtime pay results in a total gross pay of

\$1,180.00 + \$265.50 = \$1,445.50

.

Step-by-Step Solution

1

Calculate the adjusted base hourly rate.

\$26.00 + \$3.50 = \$29.50

per hour

The night shift differential is added to the standard base rate before any other multipliers are applied.

2

Calculate the regular pay for the first 40 hours.

40 \times \$29.50 = \$1,180.00

The standard workweek is 40 hours, which is paid at the regular adjusted rate.

3

Calculate the overtime hourly rate.

\$29.50 \times 1.5 = \$44.25

per hour

Overtime is paid at time-and-a-half (1.5 times the regular rate), applying to the adjusted base rate.

4

Calculate the pay for the overtime hours.

6 \times \$44.25 = \$265.50

The machinist worked 46 hours total, so 6 of those hours are considered overtime.

5

Calculate the total gross pay.

\$1,180.00 + \$265.50 = \$1,445.50

Total gross pay is the sum of the regular shift pay and the overtime pay.

Key Concept

Calculating gross pay involving base rate adjustments, shift differentials, and overtime multipliers.

Question 73Question →

When analyzing algebraic interactions, it is often necessary to determine the exact coefficient of a specific term. Find the fully expanded and simplified form of the polynomial product

(3a - 4b)^2(2a + b)

. What is the numerical coefficient of the

a^2b

term?

Show answer & explanation

Answer: -39

Answer

-39

To find the coefficient of the

a^2b

term, first expand the squared binomial

(3a - 4b)^2

to get the trinomial

9a^2 - 24ab + 16b^2

. Next, multiply this trinomial by

(2a + b)

. The specific terms that result in

a^2b

are the product of

9a^2

and

b

(which yields

9a^2b

) and the product of

-24ab

and

2a

(which yields

-48a^2b

). Combining these like terms gives

9a^2b - 48a^2b = -39a^2b

. Therefore, the numerical coefficient is -39.

Step-by-Step Solution

1

Expand the squared binomial

(3a - 4b)^2

.

9a^2 - 24ab + 16b^2

Order of operations requires resolving the exponent before multiplying by the binomial

(2a + b)

.

2

Set up the multiplication of the resulting trinomial and the binomial.

(9a^2 - 24ab + 16b^2)(2a + b)

This prepares the expression for distributing every term in the trinomial to every term in the binomial.

3

Identify and calculate only the partial products that result in an

a^2b

term.

(9a^2)(b) = 9a^2b

and

(-24ab)(2a) = -48a^2b

This is a more efficient method than fully expanding the entire polynomial if only a specific coefficient is needed.

4

Combine the identified like terms.

9a^2b - 48a^2b = -39a^2b

Combining these terms gives the final, simplified coefficient for the

a^2b

term.

Key Concept

Multiplying polynomials, expanding binomial squares, and combining like terms.

Question 74Question →

A motor pool sergeant is requisitioning maintenance supplies for his unit's vehicles. He orders $12$ quarts of synthetic oil at $\$6.75$ per quart, $4$ oil filters at $\$14.50$ each, and $3$ cans of heavy-duty degreaser at $\$5.25$ each. If he pays for the entire order using a $\$200.00$ unit procurement voucher, what is the remaining balance on the voucher in dollars?

Show answer & explanation

Answer: 45.25

Answer

45.25

The correct answer is found by first calculating the total cost for each group of items, summing these costs to determine the total purchase amount of

154.75, and then subtracting this total from the

200.00 voucher to find the remaining balance of $45.25.

Step-by-Step Solution

1

Calculate the total cost of the synthetic oil.

\$81.00

Multiply the quantity (12) by the price per quart (

\$6.75

).

2

Calculate the total cost of the oil filters.

\$58.00

Multiply the quantity (4) by the price per filter (

\$14.50

).

3

Calculate the total cost of the degreaser.

\$15.75

Multiply the quantity (3) by the price per can (

\$5.25

).

4

Calculate the total purchase amount.

\$154.75

Add the individual totals together (

\$81.00 + \$58.00 + \$15.75

).

5

Calculate the remaining balance on the voucher.

\$45.25

Subtract the total purchase amount from the initial voucher value (

\$200.00 - \$154.75

).

Key Concept

Multi-step decimal arithmetic involving unit prices and making change.

Estimated Time:1m 30s

Question 75Question →

A supply convoy is scheduled to travel a total distance of $135$ miles to a forward operating base in exactly $3$ hours and $30$ minutes. For the first $90$ minutes, the convoy travels along a secured highway at an average rate of $50$ miles per hour. For the remainder of the route, what must be the convoy's average rate of speed, in miles per hour, to arrive exactly on time?

Show answer & explanation

Answer: 30

Answer

30

The convoy must cover the remaining

60

miles in the remaining

2.0

hours, which requires an average speed of

30

miles per hour.

Step-by-Step Solution

1

Convert the given travel times from minutes to hours.

3

hours and

30

minutes =

3.5

hours.

90

minutes =

1.5

hours.

Since the speed is given in miles per hour, all time values must be in hours.

2

Calculate the distance covered on the secured highway.

50 \text{ miles/hour} \times 1.5 \text{ hours} = 75 \text{ miles}

To find out how much of the total distance has already been traveled.

3

Calculate the remaining distance to the forward operating base.

135 \text{ miles} - 75 \text{ miles} = 60 \text{ miles}

This is the distance that must be covered during the off-road portion of the route.

4

Calculate the remaining travel time available.

3.5 \text{ hours} - 1.5 \text{ hours} = 2.0 \text{ hours}

This is the time limit for completing the rest of the journey.

5

Calculate the required average speed for the remaining distance.

60 \text{ miles} \div 2.0 \text{ hours} = 30 \text{ miles per hour}

Rate equals distance divided by time (

r = \frac{d}{t}

).

Key Concept

Calculating Rate and Time

Alternative Method

You could set up an algebraic equation for the total distance:

(50 \times 1.5) + (r \times 2.0) = 135

. Solving for

r

:

75 + 2r = 135

, so

2r = 60

, which means

r = 30

.

Estimated Time:1m 30s

Question 76Question →

Two parallel lines, $L_1$ and $L_2$ , are intersected by three distinct transversals. The first transversal creates a pair of alternate interior angles that measure $(4x - 3y)^\circ$ and $(2x + y)^\circ$ . The second transversal creates a pair of consecutive (same-side) interior angles that measure $(3x + y)^\circ$ and $(5y + 36)^\circ$ . The third transversal creates a pair of corresponding angles. One of these corresponding angles measures $(x + y + z)^\circ$ , and the angle forming a linear pair with it measures $108^\circ$ . What is the value of $z$ ?

Show answer & explanation

Answer: 36

Answer

36

By applying geometric theorems for transversals (alternate interior angles are equal, same-side interior angles sum to 180), a system of equations reveals x = 24 and y = 12. Using the linear pair property, the final angle expression (x + y + z) equals 72, which isolates z to exactly 36.

Step-by-Step Solution

1

Set up an equation using the alternate interior angles.

4x - 3y = 2x + y \Rightarrow 2x = 4y \Rightarrow x = 2y

Alternate interior angles formed by a transversal intersecting parallel lines are equal.

2

Set up an equation using the consecutive (same-side) interior angles.

(3x + y) + (5y + 36) = 180 \Rightarrow 3x + 6y + 36 = 180 \Rightarrow 3x + 6y = 144

Consecutive interior angles formed by a transversal intersecting parallel lines are supplementary (sum to 180 degrees).

3

Solve the system of equations by substituting

x = 2y

into the second equation.

3(2y) + 6y = 144 \Rightarrow 6y + 6y = 144 \Rightarrow 12y = 144 \Rightarrow y = 12

. Since

x = 2y

,

x = 24

.

Substitution efficiently solves a two-variable linear system to find the individual angle components.

4

Use the linear pair to determine the measure of the corresponding angle, then solve for

z

.

(x + y + z) = 180 - 108 = 72

. Substituting known values:

24 + 12 + z = 72 \Rightarrow 36 + z = 72 \Rightarrow z = 36

.

Angles forming a linear pair are supplementary. Finding the target angle allows substitution of

x

and

y

to isolate

z

.

Key Concept

Complex systems of transversal angle relationships (alternate interior, consecutive interior, linear pairs)

Estimated Time:3m 0s

Question 77Question →

A communications platoon is distributing a shipment of $8,400$ replacement radio batteries among three forward operating bases (FOB Alpha, FOB Bravo, and FOB Charlie) in a ratio of $4:5:6$ , respectively. Based on this ratio, how many batteries will FOB Charlie receive?

Show answer & explanation

Answer: 3360

Answer

FOB Charlie will receive 3,360 batteries.

The total ratio parts sum to 15 (4 + 5 + 6). Dividing the total 8,400 batteries by 15 yields 560 batteries per part. FOB Charlie corresponds to the '6' in the ratio, so multiplying 560 by 6 gives the correct allocation of 3,360 batteries.

Step-by-Step Solution

1

Calculate the total number of ratio parts.

4 + 5 + 6 = 15

parts

To divide a total quantity in a specific ratio, you first need to determine the total number of equal parts that make up the whole.

2

Determine the amount of batteries in a single part.

8,400 \div 15 = 560

batteries per part

Dividing the total number of batteries by the total number of parts establishes the baseline value of one unit in the ratio.

3

Calculate FOB Charlie's share.

560 \times 6 = 3,360

batteries

Since FOB Charlie receives 6 parts of the ratio, multiplying the value of a single part by 6 gives their final allocation.

Key Concept

To divide a quantity into a given ratio, find the total number of parts by summing the ratio values, divide the total quantity by this sum to find the value of one part, and then multiply by the desired part's ratio value.

Question 78Question →

A tactical communications array transmits $1,800$ megabytes of encrypted data in $4.5$ minutes. At this constant rate, how many megabytes of data does the array transmit in $18$ seconds?

Show answer & explanation

Answer: 120

Answer

120

The correct answer is derived by first establishing the transmission rate of

400

megabytes per minute (

1,800 \div 4.5

). Since the required timeframe is given in seconds, it must be converted to minutes (

18 \div 60 = 0.3

minutes). Multiplying the rate by the converted time gives

120

megabytes.

Step-by-Step Solution

1

Calculate the unit transmission rate in megabytes per minute.

1,800 \div 4.5 = 400

megabytes per minute

Finding the rate per minute allows for scaling the transmission amount to any other duration.

2

Convert the target time from seconds to minutes.

18 \div 60 = 0.3

minutes

The established unit rate is in minutes, so the target time must match this temporal unit before multiplying.

3

Multiply the unit rate by the converted target time.

400 \times 0.3 = 120

megabytes

Multiplying the rate (megabytes per minute) by the time (minutes) yields the total amount of data transmitted.

Key Concept

Calculating unit rates and applying time unit conversions (seconds to minutes) to solve for a specific quantity.

Question 79Question →

The perimeter of a square courtyard is $36$ meters. What is the area of the courtyard, in square meters?

Show answer & explanation

Answer: 81

Answer

81

A square has four sides of equal length. Given a perimeter of

36

meters, each side measures

36 \div 4 = 9

meters. The area of a square is its side length squared, which is

9^2 = 81

square meters.

Step-by-Step Solution

1

Find the length of one side of the square.

36 \div 4 = 9

meters.

The perimeter of a square is the sum of its four equal sides, so dividing the total perimeter by 4 gives the length of a single side.

2

Calculate the area of the square.

9 \times 9 = 81

square meters.

The area of a square is calculated by squaring the length of one of its sides (

A = s^2

).

Key Concept

Perimeter and Area of 2D Figures

Question 80Question →

A rectangular community garden has an area of $120$ square feet. If the length of the garden is $15$ feet, what is the width of the garden, in feet?

Show answer & explanation

Answer: 8

Answer

8

The area of a rectangle is calculated by multiplying its length by its width (

A = l \times w

). To find the missing width when the area and length are known, you divide the total area by the length (

w = A \div l

). Dividing

120

by

15

results in exactly

8

feet.

Step-by-Step Solution

1

Identify the given values from the problem

Area = 120, Length = 15

To know which values to substitute into the formula for the area of a rectangle.

2

Apply the area formula for a rectangle

120 = 15 \times w

The formula relates the total area to the length and width: Area = length \times width.

3

Solve for the unknown width

w = 8

Dividing the area by the length isolates the width variable, giving the final dimension.

Key Concept

Calculating a missing dimension of a rectangle given its area and one other dimension.

Estimated Time:45s

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

Alternative Method

Answer

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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