2.6 Solve a Formula for a Specific Variable

Before you get started, take this readiness quiz.

Solve: $15 t = 120 .$
If you missed this problem, review the reference.

Solve: $6 x + 24 = 96 .$
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?

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 $t$:

1. ⓐ when $d = 520$ and $r = 65$
2. ⓑ in general

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

ⓐ when $d = 180 \text{and} t = 4$ ⓑ in general

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

ⓐ when $d = 780 \text{and} t = 12$ ⓑ in general

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

ⓐ when $A = 170$ and $b = 17$ ⓑ in general

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

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

Use the formula $I = P r t$ to find the principal, $P$:

ⓐ when $I = \$ 2,160 , r = 6 \% , t = 3 \text{years}$ ⓑ in general

Use the formula $I = P r t$ to find the principal,$P$:

ⓐ when $I = \$ 5,400 , r = 12 \% , t = 5 \text{years}$ ⓑ in general

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

ⓐ when $x = \frac{14}{3}$ ⓑ in general

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

ⓐ when $x = 4$ ⓑ in general

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

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

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

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

Solve.

Socorro drove for $4 \frac{5}{6}$ hours at 60 miles per hour. How much distance did she travel?

Solve.

Francie rode her bike for $2 \frac{1}{2}$ hours at 12 miles per hour. How far did she ride?

Solve.

Megan is taking the bus from New York City to Montreal. The distance is 380 miles and the bus travels at a steady rate of 76 miles per hour. How long will the bus ride be?

Solve.

Kareem wants to ride his bike from St. Louis to Champaign, Illinois. The distance is 180 miles. If he rides at a steady rate of 16 miles per hour, how many hours will the trip take?

Solve.

Alejandra is driving to Cincinnati, 450 miles away. If she wants to be there in 6 hours, at what rate does she need to drive?

Solve.

Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles. If the trip took 10 hours, how fast was the friend driving?

Use the formula $d = r t$.

Solve for $t$ ⓐ when $d = 240 \text{and} r = 60$ ⓑ in general

Use the formula $d = r t$.

Solve for $t$
ⓐ when $d = 175 \text{and} r = 50$
ⓑ in general

Use the formula $d = r t$.

Solve for $r$ⓐ when $d = 420 \text{and} t = 6$ⓑ in general

Use the formula $d = r t$.

Solve for $r$ⓐ when $d = 180 \text{and} t = 4.5$ⓑ in general

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

Solve for $h$
ⓐ when $A = 176 \text{and} b = 22$ⓑ in general

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

Solve for $b$ⓐ when $A = 65 \text{and} h = 13$ⓑ in general

Use the formula I = Prt.

Solve for the principal, P for
ⓐ $I = \$ 3,950 , r = 6 \% ,$$t = 5 \text{years}$ⓑ in general

Use the formula I = Prt.

Solve for the time, t for
ⓐ $I = \$ 624 , P = \$ 6,000 ,$$r = 5.2 \%$ⓑ in general

Solve.

Solve the formula $5 x + 2 y = 10$ for yⓐ when $x = 4$ⓑ in general

Solve.

Solve the formula $4 x + y = 5$ for yⓐ when $x = −3$ⓑ in general

Solve.

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

Solve.

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

Solve.

Solve the formula $9 x + y = 13$ for y.

Solve.

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

Solve.

Solve the formula $3 x + 2 y = 11$ for y.

Solve.

Solve the formula $x - y = −3$ for y.

Solve.

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

Solve.

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

Solve.

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

Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle one day was 50^o Fahrenheit. Solve for C in the formula $F = \frac{9}{5} C + 32$ to find the Celsius temperature.

Solve the equation $5 x - 2 y = 10$ for $x$ⓐ when $y = 10$ⓑ in general
ⓒ Which solution is easier for you, ⓐ or ⓑ ? Why?