9.7 Solve a Formula for a Specific Variable

Before you get started, take this readiness quiz.

Write $35$ miles per gallon as a unit rate.
If you missed this problem, review the reference.

Solve $6 x + 24 = 96 .$
If you missed this problem, review the reference.

Find the simple interest earned after $5$ years on $\$\text{1},\text{000}$ at an interest rate of $\text{4}\% .$
If you missed this problem, review the reference.

Lindsay drove for $5 \frac{1}{2}$ hours at $60$ miles per hour. How much distance did she travel?

Trinh walked for $2 \frac{1}{3}$ hours at $3$ miles per hour. How far did she walk?

Rey is planning to drive from his house in San Diego to visit his grandmother in Sacramento, a distance of $520$ miles. If he can drive at a steady rate of $65$ miles per hour, how many hours will the trip take?

Lee wants to drive from Phoenix to his brother’s apartment in San Francisco, a distance of $770$ miles. If he drives at a steady rate of $70$ miles per hour, how many hours will the trip take?

Yesenia is $168$ miles from Chicago. If she needs to be in Chicago in $3$ hours, at what rate does she need to drive?

Solve the formula $d = r t$ for $r :$

1. ⓐ when $d = 180$ and $t = 4$
2. ⓐ in general

Solve the formula $d = r t$ for $r :$

1. ⓐ when $d = 780$ and $t = 12$
2. ⓑ in general

Use the formula $A = \frac{1}{2} b h$ to solve for $h:$

1. ⓐ when $A = 170$ and $b = 17$
2. ⓑ in general

Use the formula $A = \frac{1}{2} b h$ to solve for $b :$

1. ⓐ when $A = 62$ and $h = 31$
2. ⓑ in general

Use the formula $I = P r t .$

Find $t :$ ⓐ when $I = \$\text{2},\text{160} , r = \text{6}\% , P = \$\text{12},\text{000};$ ⓑ in general

Use the formula $I = P r t .$

Find $r :$ ⓐ when $I = \$\text{5},\text{400} , P = \$\text{9},\text{000} , t = 5 \text{years}$ ⓑ in general

Solve the formula $3 x + 4 y = 10$ for $y :$

1. ⓐ when $x = 2$
2. ⓑ in general

Solve the formula $5 x + 2 y = 18$ for $y :$

1. ⓐ when $x = 4$
2. ⓑ in general

Solve the formula $P = a + b + c$ for $b .$

Solve the formula $P = a + b + c$ for $c .$

Solve the formula $7 x + y = 11$ for $y .$

Solve the formula $11 x + y = 8$ for $y .$

Solve the formula $4 x + 7 y = 9$ for $y .$

Solve the formula $5 x + 8 y = 1$ for $y .$

Solve.

Steve drove for $8 \frac{1}{2}$ hours at $72$ miles per hour. How much distance did he travel?

Solve.

Yuki walked for $1 \frac{3}{4}$ hours at $4$ miles per hour. How far did she walk?

Solve.

Connor wants to drive from Tucson to the Grand Canyon, a distance of $338$ miles. If he drives at a steady rate of $52$ miles per hour, how many hours will the trip take?

Solve.

Aurelia is driving from Miami to Orlando at a rate of $65$ miles per hour. The distance is $235$ miles. To the nearest tenth of an hour, how long will the trip take?

Solve.

Javier is driving to Bangor, Maine, which is $240$ miles away from his current location. If he needs to be in Bangor in $4$ hours, at what rate does he need to drive?

Solve.

Aisha took the train from Spokane to Seattle. The distance is $280$ miles, and the trip took $3.5$ hours. What was the speed of the train?

Use the formula. $d = r t .$

Solve for $t :$

1. ⓐ when $d = 350$ and $r = 70$
2. ⓑ in general

Use the formula. $d = r t .$

Solve for $t :$

1. ⓐ when $d = 510$ and $r = 60$
2. ⓑ in general

Use the formula. $d = r t .$

Solve for $r :$

1. ⓐ when $d = 204$ and $t = 3$
2. ⓑ in general

Use the formula. $d = r t .$

Solve for $r :$

1. ⓐ when $d = 160$ and $t = 2.5$
2. ⓑ in general

Use the formula $A = \frac{1}{2} b h .$

Solve for $b :$

1. ⓐ when $A = 126$ and $h = 18$
2. ⓑ in general

Use the formula $A = \frac{1}{2} b h .$

Solve for $h :$

1. ⓐ when $A = 375$ and $b = 25$
2. ⓑ in general

Use the formula $I = P r t .$

Solve for the principal, $P$ for:

1. ⓐ $I = \$\text{5},\text{480}$, $r = \text{4}\%$, $t = 7 \text{years}$
2. ⓑ in general

Use the formula $I = P r t .$

Solve for the time, $t$ for:

1. ⓐ $I = \$\text{2},\text{376}$, $P = \$\text{9},\text{000}$, $r = 4.4 \%$
2. ⓑ in general

Solve.

Solve the formula $2 x + 3 y = 12$ for $y :$

1. ⓐ when $x = 3$
2. ⓑ in general

Solve.

Solve the formula $3 x + y = 7$ for $y :$

1. ⓐ when $x = −2$
2. ⓑ in general

Solve.

Solve $a + b = 90$ for $b .$

Solve.

Solve $180 = a + b + c$ for $a .$

Solve.

Solve the formula $8 x + y = 15$ for $y .$

Solve.

Solve the formula $- 4 x + y = −6$ for $y .$

Solve.

Solve the formula $4 x + 3 y = 7$ for $y .$

Solve.

Solve the formula $x - y = −4$ for $y .$

Solve.

Solve the formula $P = 2 L + 2 W$ for $L .$

Solve.

Solve the formula $C = \pi d$ for $d .$

Solve.

Solve the formula $V = L W H$ for $L .$

Converting temperature While on a tour in Greece, Tatyana saw that the temperature was $\text{40}°$ Celsius. Solve for $F$ in the formula $C = \frac{5}{9} \left(F - 32\right)$ to find the temperature in Fahrenheit.

Solve the equation $2 x + 3 y = 6$ for $y :$

1. ⓐ when $x = −3$
2. ⓑ in general
3. ⓒ Which solution is easier for you? Explain why.

Solve.

How has your attitude towards solving word problems changed as a result of working through this chapter? Explain.

Solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question.

Three-fourths of the people at a concert are children. If there are $87$ children, what is the total number of people at the concert?

Solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question.

Reza was very sick and lost $\text{15}\%$ of his original weight. He lost $27$ pounds. What was his original weight?

Solve each number word problem.

The sum of a number and three is forty-one. Find the number.

Solve each number word problem.

One number is nine less than another. Their sum is twenty-seven. Find the numbers.

Solve each coin word problem.

Francie has $\$\text{4}.\text{35}$ in dimes and quarters. The number of dimes is $5$ more than the number of quarters. How many of each coin does she have?

Solve each coin word problem.

Paulette has $\$\text{140}$ in $\$\text{5}$ and $\$\text{10}$ bills. The number of $\$\text{10}$ bills is one less than twice the number of $\$\text{5}$ bills. How many of each does she have?

Solve each ticket or stamp word problem.

A church luncheon made $\$\text{842} .$ Adult tickets cost $\$\text{10}$ each and children’s tickets cost $\$\text{6}$ each. The number of children was $12$ more than twice the number of adults. How many of each ticket were sold?

Solve each ticket or stamp word problem.

Ana spent $\$\text{4}.\text{06}$ buying stamps. The number of $\$\text{0}.\text{41}$ stamps she bought was $5$ more than the number of $\$\text{0}.\text{26}$ stamps. How many of each did she buy?

Solve using properties of angles.

What is the supplement of a $\text{48}°$ angle?

Solve using properties of angles.

Two angles are complementary. The smaller angle is $\text{24}°$ less than the larger angle. Find the measures of both angles.

Solve using properties of triangles.

The measures of two angles of a triangle are $22$ and $85$ degrees. Find the measure of the third angle.

Solve using properties of triangles.

One angle of a triangle is $\text{30}°$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.

side $x$

Would you measure each item using linear, square, or cubic measure?

amount of sand in a sandbag

Would you measure each item using linear, square, or cubic measure?

size of a patio

Find the ⓐ perimeter ⓑ area of each rectangle

The length of a rectangle is $42$ meters and the width is $28$ meters.

Find the ⓐ perimeter ⓑ area of each rectangle

A sidewalk in front of Kathy’s house is in the shape of a rectangle $4$ feet wide by $45$ feet long.

Solve.

Find the length of a rectangle with perimeter of $220$ centimeters and width of $85$ centimeters.

Solve.

The area of a rectangle is $2356$ square meters. The length is $38$ meters. What is the width?

Solve.

The length of a rectangle is $12$ centimeters more than the width. The perimeter is $74$ centimeters. Find the length and the width.

Solve using the properties of triangles.

Find the area of a triangle with base $18$ inches and height $15$ inches.

Solve using the properties of triangles.

A triangular road sign has base $30$ inches and height $40$ inches. What is its area?

Solve using the properties of triangles.

A tile in the shape of an isosceles triangle has a base of $6$ inches. If the perimeter is $20$ inches, find the length of each of the other sides.

Solve using the properties of triangles.

The perimeter of a triangle is $59$ feet. One side of the triangle is $3$ feet longer than the shortest side. The third side is $5$ feet longer than the shortest side. Find the length of each side.

Solve using the properties of trapezoids.

The height of a trapezoid is $8$ feet and the bases are $11$ and $14$ feet. What is the area?

Solve using the properties of trapezoids.

Find the area of the trapezoid with height $25$ meters and bases $32.5$ and $21.5$ meters.

Solve using the properties of circles. Round answers to the nearest hundredth.

A circular mosaic has radius $3$ meters. Find the

1. ⓐ circumference
2. ⓑ area of the mosaic

Solve using the properties of circles. Round answers to the nearest hundredth.

Find the diameter of a circle with circumference $150.72$ inches.

Find the

1. ⓐ volume
2. ⓑ surface area of the rectangular solid

a rectangular solid with length $14$ centimeters, width $4.5$ centimeters, and height $10$ centimeters

Find the

1. ⓐ volume
2. ⓑ surface area of the rectangular solid

a cube of tofu with sides $2.5$ inches

Find the

1. ⓐ volume
2. ⓑ surface area of the sphere.

a sphere with radius $4$ yards

Find the

1. ⓐ volume
2. ⓑ surface area of the sphere.

a baseball with radius $1.45$ inches

Find the

1. ⓐ volume
2. ⓑ surface area of the cylinder

a cylinder with radius $2$ yards and height $6$ yards

Find the

1. ⓐ volume
2. ⓑ surface area of the cylinder

a juice can with diameter $8$ centimeters and height $15$ centimeters

Find the volume of the cone.

a cone with height $5$ meters and radius $1$ meter

Find the volume of the cone.

a cone-shaped water cup with diameter $2.6$ inches and height $2.6$ inches

Solve using the formula for distance, rate, and time.

A plane flew $4$ hours at $380$ miles per hour. What distance was covered?

Solve using the formula for distance, rate, and time.

Jack is driving from Bangor to Portland at a rate of $68$ miles per hour. The distance is $107$ miles. To the nearest tenth of an hour, how long will the trip take?

Use the formula $d = r t .$

Solve for $t :$

1. ⓐ when $d = 403$ and $r = 65$
2. ⓑ in general

Use the formula $A = \frac{1}{2} b h .$

Solve for $b :$

1. ⓐ when $A = 416$ and $h = 32$
2. ⓑ in general

Use the formula $I = P r t .$

Solve for the principal, $P ,$ for:

1. ⓐ $I = \$\text{720}$, $r = \text{4}\%$, $t = 3 \text{years}$
2. ⓑ in general

Solve.

Solve the formula $6 x + 5 y = 20$ for $y :$

1. ⓐ when $x = 0$
2. ⓑ in general

Solve.

Solve $a + b = 90$ for $a .$

Solve.

Solve the formula $4 x + y = 17$ for $y .$

Solve.

Solve the formula $P = 2 L + 2 W$ for $W .$

The sum of $13$ and twice a number is $- 19 .$ Find the number.

Bonita has $\$\text{2}.\text{95}$ in dimes and quarters in her pocket. If she has $5$ more dimes than quarters, how many of each coin does she have?

Find the complement of a $\text{52}°$ angle.

The perimeter of an equilateral triangle is $145$ feet. Find the length of each side.

A triangular poster has base $80$ centimeters and height $55$ centimeters. Find the area of the poster.

A circular pool has diameter $90$ inches. What is its circumference? Round to the nearest tenth.

Find the volume of a rectangular room with width $12$ feet, length $15$ feet, and height $8$ feet.

A traffic cone has height $75$ centimeters. The radius of the base is $20$ centimeters. Find the volume of the cone. Round to the nearest tenth.

The Catalina Express takes $1 \frac{1}{2}$ hours to travel from Long Beach to Catalina Island, a distance of $22$ miles. To the nearest tenth, what is the speed of the boat?

Solve the formula $A = \frac{1}{2} b h$ for $h :$

1. ⓐ when $A = 1716$ and $b = 66$
2. ⓑ in general