Tüm alıştırma soruları

Consider the following system of linear equations:

4(x - 2) + y = 3x

2x - 3(y + 1) = -2

What is the value of the expression $x - y$ ?

Cevabı ve açıklamayı göster

Cevap: 2

Cevap

2

The correct answer is derived by first simplifying both equations into standard form (x + y = 8 and 2x - 3y = 1). By applying the elimination method, we find the system's solution is x = 5 and y = 3. Finally, evaluating the specific requested expression gives us x - y = 5 - 3 = 2.

Adım Adım Çözüm

1

Simplify the first equation.

x + y = 8

Equations must be in standard form to easily apply elimination or substitution.

2

Simplify the second equation.

2x - 3y = 1

Expanding the terms and grouping variables on one side creates the standard form.

3

Multiply the simplified first equation by 3.

3x + 3y = 24

This aligns the y-coefficients (3y and -3y) for the elimination method.

4

Add the modified first equation to the simplified second equation.

5x = 25

Adding the equations eliminates the y variable, allowing us to solve for x.

5

Divide both sides by 5.

x = 5

Isolates the variable x.

6

Substitute x = 5 into the simplified first equation (x + y = 8).

y = 3

This finds the value of the remaining variable, y.

7

Evaluate the target expression (x - y).

5 - 3 = 2

The question specifically asks for the difference between x and y, not just their individual values.

Anahtar Kavram

Solving systems of linear equations involving pre-simplification

Soru 82Soru →

Two cyclists, Sarah and Mike, start at opposite ends of a $60$ -mile trail and ride directly toward each other. Sarah rides at a constant speed of $12$ mph, and Mike rides at a constant speed of $18$ mph. How many hours will it take for them to meet?

Cevabı ve açıklamayı göster

Cevap: 2

Cevap

2

Because the cyclists are moving directly toward each other, their gap closes at a combined rate of

30

mph (

12

mph +

18

mph). Dividing the total initial distance of

60

miles by this combined rate yields exactly

2

hours.

Adım Adım Çözüm

1

Calculate the combined relative speed.

30 mph

When objects move toward each other from opposite directions, their relative speed is the sum of their individual speeds (

12 + 18 = 30

).

2

Calculate the time required to meet.

2 hours

Using the formula Time = Distance / Rate, divide the total distance (

60

miles) by the relative speed (

30

mph).

Anahtar Kavram

Relative Motion and Catch-Up Scenarios

Soru 83Soru →

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

Cevabı ve açıklamayı göster

Cevap: 775

Cevap

775

The correct answer is determined by first finding the sales amount eligible for commission (

14,500 -

8,000 =

6,500). Next, calculate the 5% commission on this excess amount (

6,500 \times 0.05 =

325). Finally, add this commission to the fixed weekly base pay to find the total gross pay (

450 +

325 =

775).

Adım Adım Çözüm

1

Determine the portion of sales subject to the commission rate.

\$14,500 - \$8,000 = \$6,500

The commission is only applied to the sales volume that surpasses the $8,000 threshold.

2

Calculate the commission earned on the excess sales.

\$6,500 \times 0.05 = \$325

The representative earns 5% on the eligible sales amount.

3

Calculate the total gross pay.

\$450 + \$325 = \$775

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

Anahtar Kavram

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

Soru 84Soru →

A competitive swimmer is walking around the outer edge of a rectangular pool to warm up. If the pool has a length of $50$ meters and a width of $25$ meters, what is the total perimeter of the pool, in meters?

Cevabı ve açıklamayı göster

Cevap: 150

Cevap

The total perimeter of the pool is 150 meters.

The perimeter of a rectangle is found by adding the lengths of all four sides. Using the formula

P = 2l + 2w

, we calculate

2(50) + 2(25) = 150

meters.

Adım Adım Çözüm

1

Identify the shape and the goal.

The shape is a rectangle and we need to find its perimeter.

Understanding what needs to be calculated determines the correct formula.

2

Recall the perimeter formula for a rectangle.

P = 2l + 2w

or

P = 2(l + w)

The perimeter is the total distance around the outside of the shape.

3

Substitute the given dimensions into the formula.

P = 2(50) + 2(25)

The length (

l

) is

50

and the width (

w

) is

25

.

4

Perform the arithmetic operations.

100 + 50 = 150

Multiplying the terms and adding them together yields the final perimeter.

Anahtar Kavram

Perimeter of Rectangles

Soru 85Soru →

A cafe sells muffins and scones. A customer purchases $2$ muffins and $1$ scone for a total of $11$ dollars. If the price of one scone is $4$ dollars less than the price of $3$ muffins, what is the price of one scone in dollars?

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

The price of one scone is

5

dollars.

By translating the word problem into a system of two equations (

2m + s = 11

and

s = 3m - 4

) and using substitution, we find that

m = 3

and

s = 5

. Thus, the price of one scone is

5

.

Adım Adım Çözüm

1

Define variables and set up the equations based on the word problem.

Let

m

= price of a muffin and

s

= price of a scone. The equations are

2m + s = 11

and

s = 3m - 4

.

Translating the text into algebraic equations allows us to solve for the unknown values.

2

Substitute the expression for

s

from the second equation into the first equation.

2m + (3m - 4) = 11

This eliminates the variable

s

, leaving an equation with only one variable,

m

.

3

Solve the resulting equation for

m

.

5m - 4 = 11 \Rightarrow 5m = 15 \Rightarrow m = 3

Isolating

m

gives us the price of one muffin.

4

Substitute the value of

m

back into the equation for

s

.

s = 3(3) - 4 = 9 - 4 = 5

This calculates the price of the scone, which is the final requested value.

Anahtar Kavram

Solving systems of linear equations using the substitution method.

Soru 86Soru →

A field kitchen consumes $15$ pounds of coffee over a $4$ -hour breakfast service. What is the unit rate of coffee consumption, in ounces per hour?

Cevabı ve açıklamayı göster

Cevap: 60

Cevap

60

The unit rate is found by first converting the total weight into the requested units. Since 1 pound equals 16 ounces, 15 pounds is equal to 240 ounces. Dividing this 240 ounces by the 4 hours of service gives the correct unit rate of 60 ounces per hour.

Adım Adım Çözüm

1

Convert the total coffee weight from pounds to ounces.

15 \times 16 = 240

ounces

The question specifically asks for the rate in ounces per hour, and there are 16 ounces in 1 pound.

2

Calculate the unit rate by dividing the total ounces by the total hours.

240 \div 4 = 60

ounces per hour

A unit rate represents the quantity of one variable per single unit of another variable, found here by dividing total consumption by total time.

Anahtar Kavram

Calculating Unit Rates with Unit Conversions

Soru 87Soru →

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

Cevabı ve açıklamayı göster

Cevap: 18

Cevap

18

The simple interest formula is

I = P \times r \times t

. Substituting the given values gives

135 = 2500 \times 0.036 \times t

. Solving for

t

yields

1.5

years. Multiplying by 12 converts this to exactly 18 months.

Adım Adım Çözüm

1

Identify the simple interest formula and the given values.

I = P \times r \times t

, where

I = \$135

,

P = \$2,500

, and

r = 0.036

.

To set up the equation to solve for the unknown time variable.

2

Substitute the values into the formula and simplify.

135 = 2500 \times 0.036 \times t

, which simplifies to

135 = 90t

.

To isolate the term with the unknown variable.

3

Solve for the time

t

in years.

t = 135 / 90 = 1.5

years.

The standard simple interest formula calculates time in years.

4

Convert the time from years to months.

1.5 \times 12 = 18

months.

The question specifically asks for the duration in months.

Anahtar Kavram

Simple Interest

Soru 88Soru →

A rectangular metallic sheet has a length of $28$ inches and a width of $15$ inches. A triangular metallic sheet has the exact same area. If the base of the triangular sheet is $24$ inches, what is its height, in inches?

Cevabı ve açıklamayı göster

Cevap: 35

Cevap

35

The correct height is found by first determining the area of the rectangle (

28 \times 15 = 420

). Since the triangle shares this exact area and has a given base of

24

, solving the triangle area formula

420 = \frac{1}{2}(24)h

yields

12h = 420

, which simplifies to

h = 35

.

Adım Adım Çözüm

1

Calculate the area of the rectangular sheet.

Area = 420 square inches

The area of the rectangle is required to find the area of the triangle, as the problem explicitly states their areas are equal.

2

Set up the area equation for the triangular sheet.

420 = 0.5 * 24 * h

Substituting the known area and base into the triangle area formula allows us to solve for the unknown height.

3

Solve the algebraic equation for the height (h).

h = 35

Simplifying 420 = 12h by dividing both sides by 12 isolates the height variable.

Anahtar Kavram

Calculating and equating the area of different 2D figures using standard area formulas.

Tahmini Süre:1m 0s

Soru 89Soru →

A reservist earns a base pay of $\$115.50$ per drill period. During a weekend drill, she completes $4$ drill periods. Additionally, she receives a travel allowance of $\$0.65$ per mile for her $42$ -mile round trip. What is her total compensation for the weekend in dollars?

Cevabı ve açıklamayı göster

Cevap: 489.3

Cevap

489.30

The total compensation is the sum of the drill pay (

4 \times \$115.50 = \$462.00

) and the travel allowance (

42 \times \$0.65 = \$27.30

), which results in a final total of

\$489.30

.

Adım Adım Çözüm

1

Calculate the total pay for the drill periods.

\$462.00

The reservist gets paid

\$115.50

for each of the

4

drill periods.

2

Calculate the total travel allowance.

\$27.30

The travel allowance is calculated at a rate of

\$0.65

per mile for a total of

42

miles.

3

Add the drill pay and travel allowance together.

\$489.30

The total compensation is the sum of all earnings for the weekend.

Anahtar Kavram

Decimal operations and currency word problems involving rates and total quantities.

Soru 90Soru →

An armored vehicle traverses an $18$ -mile desert route. It travels the first $10$ miles at a constant speed of $20$ miles per hour. If the vehicle completes the entire route in exactly $45$ minutes, what is its speed in miles per hour for the remaining distance?

Cevabı ve açıklamayı göster

Cevap: 32

Cevap

The speed for the remaining distance is

32

miles per hour.

To find the unknown speed, you must isolate the distance and time for the final segment. First, the time for the

10

-mile stretch is calculated as

0.5

hours, which is equivalent to

30

minutes. Subtracting this from the total

45

minutes leaves

15

minutes (or

0.25

hours) to travel the remaining

8

miles. Dividing the

8

miles by the

0.25

hours of remaining time yields a final speed of

32

miles per hour.

Adım Adım Çözüm

1

Calculate the time for the first segment.

10 \text{ miles} \div 20 \text{ mph} = 0.5 \text{ hours}

You need to know how much time was spent on the first segment to determine the time left for the remainder of the route.

2

Convert the first segment's time into minutes.

0.5 \text{ hours} \times 60 \text{ minutes/hour} = 30 \text{ minutes}

The total time is provided in minutes (

45

minutes), so making the units consistent allows you to easily subtract and find the remaining time.

3

Find the remaining time available.

45 \text{ minutes} - 30 \text{ minutes} = 15 \text{ minutes}

This step determines exactly how much time the vehicle has to complete the rest of the route.

4

Convert the remaining time into hours.

15 \text{ minutes} \div 60 \text{ minutes/hour} = 0.25 \text{ hours}

Since the requested final speed must be in miles per hour, the time value needs to be expressed in hours.

5

Determine the remaining distance.

18 \text{ miles} - 10 \text{ miles} = 8 \text{ miles}

This is the physical distance the vehicle must cover during the final

15

minutes.

6

Calculate the speed for the final segment.

8 \text{ miles} \div 0.25 \text{ hours} = 32 \text{ mph}

Dividing the remaining distance by the remaining time gives the required speed.

Anahtar Kavram

Calculating unknown rates in multi-part trips by finding intermediate distances and times, and converting units correctly.

Soru 91Soru →

A painter is marking a new parallelogram-shaped crosswalk on a street. The base of the parallelogram is $45$ feet long, and the perpendicular height across the street is $20$ feet. What is the total area of the crosswalk, in square feet?

Cevabı ve açıklamayı göster

Cevap: 900

Cevap

900

The area of a parallelogram is calculated by multiplying its base by its perpendicular height. Given a base of

45

feet and a height of

20

feet, the area is

45 \times 20 = 900

square feet.

Adım Adım Çözüm

1

Identify the relevant formula

A = b \times h

The area of a parallelogram is the product of its base and perpendicular height.

2

Substitute the given values into the formula

A = 45 \times 20

The base (

b

) is given as

45

feet and the height (

h

) is

20

feet.

3

Calculate the final area

900

Multiplying

45

by

20

gives

900

.

Anahtar Kavram

Area of a Parallelogram

Tahmini Süre:30s

Soru 92Soru →

A cyclist is riding on a paved trail at a constant speed of $15 \text{ miles per hour}$ . At this rate, how many miles will the cyclist travel in $40 \text{ minutes}$ ?

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

10

The distance is found by matching the time units to the speed units. First, convert

40 \text{ minutes}

into

\frac{2}{3} \text{ hours}

. Then, multiply the speed (

15 \text{ mph}

) by the time (

\frac{2}{3} \text{ hours}

) to get exactly 10 miles.

Adım Adım Çözüm

1

Convert the travel time from minutes to hours.

40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}

The speed is given in miles per hour, so the time must be converted to hours before using it in the distance formula.

2

Calculate the total distance traveled.

15 \times \frac{2}{3} = 10 \text{ miles}

Distance is equal to the rate (speed) multiplied by the time (

d = r \times t

).

Anahtar Kavram

Unit conversions for time in rate problems

Soru 93Soru →

An artist is framing a rectangular painting that measures $10$ inches in length and $8$ inches in width. The frame has a uniform width of $2$ inches on all sides. What is the total area of the frame itself, in square inches?

Cevabı ve açıklamayı göster

Cevap: 88

Cevap

88

To find the area of the frame, subtract the area of the painting from the total area of the painting with the frame included. Because the frame is 2 inches wide on all sides, the overall dimensions increase by 4 inches in both directions. The outer rectangle is 14 inches by 12 inches (168 square inches). The inner painting is 10 inches by 8 inches (80 square inches). Subtracting the inner area from the outer area gives 168 - 80 = 88 square inches.

Adım Adım Çözüm

1

Determine the outer dimensions of the framed painting.

Outer length = 14 inches, Outer width = 12 inches

The frame adds 2 inches to both the left and right sides (total of 4 inches to length), and 2 inches to both the top and bottom (total of 4 inches to width).

2

Calculate the total combined area of the painting and the frame.

168 square inches

Area of a rectangle is length multiplied by width (14 * 12).

3

Calculate the area of the inner painting.

80 square inches

The painting dimensions are 10 by 8 (10 * 8).

4

Subtract the inner area from the total area to find the area of the frame.

88 square inches

The frame is the region between the outer and inner rectangles.

Anahtar Kavram

The area of a border or frame is found by calculating the total outer area and subtracting the inner area.

Soru 94Soru →

To fund a certification course, a network administrator invested a specific amount of money into a standard savings account yielding $5\%$ annual simple interest. After leaving the funds untouched for $30$ months, the investment generated exactly $\$375$ in interest alone. What was the initial amount deposited into the account?

Cevabı ve açıklamayı göster

Cevap: 3000

Cevap

The initial amount deposited was $3,000.

The principal is found by dividing the interest earned by the product of the annual interest rate and the time in years. Converting

30

months to

2.5

years and using the

5\%

rate as

0.05

, the calculation is

375 \div (0.05 \times 2.5) = 3000

.

Adım Adım Çözüm

1

Identify the given variables for the simple interest formula.

I = 375

,

r = 0.05

,

t = 30

months.

The formula requires these values to solve for the unknown principal

P

.

2

Convert the time period from months to years.

t = \frac{30}{12} = 2.5

years.

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

3

Set up the simple interest equation.

375 = P \times 0.05 \times 2.5

Using the standard simple interest formula

I = P \times r \times t

.

4

Solve for the principal

P

.

P = \frac{375}{0.125} = 3000

Isolating

P

provides the final initial deposit amount.

Anahtar Kavram

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

Soru 95Soru →

A topographic surveying team has mapped $\frac{5}{8}$ of a designated training sector. What percentage of the training sector remains to be mapped?

Cevabı ve açıklamayı göster

Cevap: 37.5

Cevap

37.5

The correct answer is 37.5 because the remaining fraction of the sector is

\frac{3}{8}

. Since

\frac{1}{8}

equals

12.5\%

, multiplying by 3 gives

37.5\%

.

Adım Adım Çözüm

1

Calculate the fraction of the training sector that remains to be mapped.

1 - \frac{5}{8} = \frac{3}{8}

The entire sector represents 1 whole. Subtracting the mapped portion gives the remaining unmapped portion.

2

Recall the percentage equivalent of the base fraction

\frac{1}{8}

.

\frac{1}{8} = 12.5\%

Memorizing common fractional equivalents like eighths, thirds, and fourths is essential for solving ASVAB problems quickly without a calculator.

3

Calculate the percentage equivalent for

\frac{3}{8}

.

3 \times 12.5\% = 37.5\%

Since

\frac{3}{8}

is three times the base fraction

\frac{1}{8}

, multiply the corresponding percentage by 3.

Anahtar Kavram

Converting common fractions to percentages and solving part-to-whole word problems.

Tahmini Süre:1m 0s

Soru 96Soru →

A specialized water purification system takes $3$ hours and $20$ minutes to process one complete cycle. If an engineering detachment runs the system continuously for exactly $2.5$ days, how many complete cycles will the system finish?

Cevabı ve açıklamayı göster

Cevap: 18

Cevap

18

The correct answer is found by establishing a common unit of time (minutes) for both the total duration and the cycle length. First, converting the

2.5

days of total operation into hours gives

60

hours, which equals

3600

minutes. Next, converting the

3

hour and

20

minute cycle duration into minutes yields

200

minutes. Finally, dividing the total available time (

3600

minutes) by the cycle time (

200

minutes) results in exactly

18

complete cycles.

Adım Adım Çözüm

1

Convert the total continuous running time from days to hours.

2.5 \times 24 = 60

hours

To establish a smaller standard unit of time to match the cycle duration.

2

Convert the total operating hours into minutes.

60 \times 60 = 3600

minutes

Minutes will serve as the common baseline unit for the calculation.

3

Convert the required time for a single cycle into minutes.

3 \times 60 = 180

minutes;

180 + 20 = 200

minutes

To express the cycle duration in the exact same unit as the total running time.

4

Calculate the total number of completed cycles by dividing the total minutes by the cycle minutes.

3600 \div 200 = 18

cycles

This division determines how many

200

-minute intervals fit within the

3600

-minute window.

Anahtar Kavram

Multi-step time unit conversions and calculating work rate.

Soru 97Soru →

A direct-current (DC) communication antenna heater operates from a $48\text{ V}$ power source and dissipates $96\text{ W}$ of electrical power. What is the electrical resistance of the heater in ohms ( $\Omega$ )?

Cevabı ve açıklamayı göster

Cevap: 24

Cevap

The electrical resistance of the antenna heater is

24\ \Omega

.

According to Watt's Law, power is related to voltage and resistance by

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

. Rearranging this formula to solve for resistance gives

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

. Substituting

48\text{ V}

for voltage and

96\text{ W}

for power yields

R = \frac{48^2}{96} = \frac{2304}{96} = 24\ \Omega

.

Adım Adım Çözüm

1

Select the appropriate form of Watt's Law connecting power (

P

), voltage (

V

), and resistance (

R

).

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

The circuit parameters given are voltage and power, with resistance as the unknown variable.

2

Rearrange the formula to isolate resistance (

R

).

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

Algebraic isolation of

R

allows direct calculation from the known values.

3

Substitute

V = 48\text{ V}

and

P = 96\text{ W}

into the rearranged formula and compute the result.

R = \frac{48^2}{96} = \frac{2304}{96} = 24\ \Omega

Simplifying the arithmetic yields the exact resistance value.

Anahtar Kavram

Watt's Law relates power, voltage, and resistance through the formula

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

, which rearranges to

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

.

Alternatif Yöntem

First find the current drawn by the heater using

I = \frac{P}{V} = \frac{96\text{ W}}{48\text{ V}} = 2\text{ A}

. Then apply Ohm's Law to determine the resistance:

R = \frac{V}{I} = \frac{48\text{ V}}{2\text{ A}} = 24\ \Omega

.

Tahmini Süre:1m 0s

Soru 98Soru →

A technician connects a $10\text{ }\mu\text{F}$ capacitor in parallel with a $22\text{ }\mu\text{F}$ capacitor in a power supply filter circuit. What is the total equivalent capacitance of this combination in microfarads ( $\mu\text{F}$ )?

Cevabı ve açıklamayı göster

Cevap: 32

Cevap

32 uF

When capacitors are connected in parallel, their total capacitance is the direct sum of the individual capacitances:

C_{\text{total}} = C_1 + C_2

. Adding

10\text{ }\mu\text{F}

and

22\text{ }\mu\text{F}

results in a total equivalent capacitance of

32\text{ }\mu\text{F}

.

Adım Adım Çözüm

1

Identify the circuit configuration and the relevant formula for equivalent capacitance.

The two capacitors are connected in parallel, meaning their total capacitance is the sum of their individual capacitances:

C_{\text{total}} = C_1 + C_2

.

Connecting capacitors in parallel effectively increases the total plate surface area, allowing more electric charge to be stored at a given voltage.

2

Calculate the sum of the individual capacitances.

C_{\text{total}} = 10\text{ }\mu\text{F} + 22\text{ }\mu\text{F} = 32\text{ }\mu\text{F}

.

Direct addition yields the total equivalent capacitance.

Anahtar Kavram

Total capacitance in a parallel circuit is calculated by directly adding the individual capacitances (

C_{\text{total}} = C_1 + C_2 + \dots

).

Tahmini Süre:45s

Soru 99Soru →

A portable two-way radio is powered by four $1.5\text{ V}$ battery cells connected in series aiding. What is the total electromotive force (EMF) supplied to the radio circuit, in volts?

Cevabı ve açıklamayı göster

Cevap: 6

Cevap

The total electromotive force supplied is

6.0\text{ V}

(or

6\text{ V}

).

Connecting direct current (DC) cells in series aiding connects the positive terminal of each cell to the negative terminal of the next, causing their individual potential differences to combine additively. Therefore, four

1.5\text{ V}

cells produce a total EMF of

4 \times 1.5\text{ V} = 6.0\text{ V}

.

Adım Adım Çözüm

1

Apply the series voltage addition principle

V_{\text{total}} = V_1 + V_2 + V_3 + V_4

When voltage sources are connected in series aiding, their individual potential differences add together directly to provide the total electromotive force.

2

Perform the calculation for four identical

1.5\text{ V}

cells

V_{\text{total}} = 4 \times 1.5\text{ V} = 6.0\text{ V}

Multiplying the single-cell potential by the quantity of series-connected cells yields the overall circuit EMF.

Anahtar Kavram

Series Voltage Addition and Electromotive Force (EMF)

Tahmini Süre:45s

Soru 100Soru →

A fuel tank on a generator is initially $\frac{7}{8}$ full. After the generator consumes $15$ gallons of fuel, the tank is exactly $\frac{1}{4}$ full. What is the total capacity of the fuel tank in gallons?

Cevabı ve açıklamayı göster

Cevap: 24

Cevap

The total capacity of the fuel tank is 24 gallons.

The correct answer is derived by finding the difference in the fraction of the tank's capacity (

\frac{7}{8} - \frac{1}{4} = \frac{5}{8}

). Since this

\frac{5}{8}

portion corresponds to

15

gallons, the total capacity is found by dividing

15

by

\frac{5}{8}

, which yields

24

gallons.

Adım Adım Çözüm

1

Find a common denominator for the given fractions.

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

To subtract the fractions, they must have the same denominator.

2

Calculate the fraction of the tank that was consumed by the generator.

\frac{7}{8} - \frac{2}{8} = \frac{5}{8}

The difference between the initial and final fuel levels represents the exact amount consumed.

3

Set up an algebraic equation linking the fraction consumed to the actual volume in gallons.

\frac{5}{8} \times \text{Capacity} = 15

We know that

\frac{5}{8}

of the total capacity corresponds directly to the

15

gallons used.

4

Solve the equation for the total capacity.

15 \times \frac{8}{5} = 24

Multiplying by the reciprocal of the fraction isolates the capacity variable.

Anahtar Kavram

Applying fraction subtraction with unlike denominators and solving a missing-value equation using a reciprocal.

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