# Exercises: Solve a Formula for a Specific Variable (3.6)

## Exercises: Use the Distance, Rate, and Time Formula

Instructions: For questions 1-12, solve.

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

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

$290$ miles

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

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

$30$ miles

5. 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?

6. 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?
Solution

$5$ hours

7. 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?

8. 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?
Solution

$11.25$ hours

9. Javier is driving to Bangor, $240$ miles away. If he needs to be in Bangor in $4$ hours, at what rate does he need to drive?

10. 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?
Solution

$75$ mph

11. 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?

12. 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?
Solution

$75$ mph

## Exercises: Solve a Formula for a Specific Variable

Instructions: For questions 13-20, use the formula $d=rt$.

13. Solve for $t$

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

14. Solve for $t$

a. when $d=240$ and $r=60$
b. in general

Solution

a. $t=4$
b. $t=\frac{d}{r}$

15. Solve for $t$

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

16. Solve for $t$

a. when $d=175$ and $r=50$
b. in general

Solution

a. $t=3.5$
b. $t=\frac{d}{r}$

17. Solve for $r$

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

18. Solve for $r$

a. when $d=420$ and $t=6$
b. in general

Solution

a. $r=70$
b. $r=\frac{d}{t}$

19. Solve for $r$

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

20. Solve for $r$

a. when $d=180$ and $t=4.5$
b. in general

Solution

a. $r=40$
b. $r=\frac{d}{t}$

## Exercises: Use the Area of a Triangle Formula (Area, Base, and Height)

Instructions: For questions 21-24, use the formula $A=\frac{1}{2}bh$.

21. Solve for $b$

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

22. Solve for $h$

a. when $A=176$ and $b=22$
b. in general

Solution

a. $h=16$
b. $h=\frac{2A}{b}$

23. Solve for $h$

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

24. Solve for $b$

a. when $A=65$ and $h=13$
b. in general

Solution

a. $b=10$
b. $b=\frac{2A}{h}$

## Exercises: Use the Interest, Principal, Rate, and Time Formula

Instructions: For questions 25-28, use the formula $I=Prt$

25. Solve for the principal, $P$ for

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

26. Solve for the principal, $P$ for

a. $I=3,950,r=6\%,t=5\text{ years}$
b. in general

Solution

a. $P=13,166.67$
b. $P=\frac{I}{rt}$

27. Solve for the time, $t$ for

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

28. Solve for the time, $t$ for

a. $I=624,P=6,000,r=5.2\%$
b. in general

Solution

a. $t=2$ years
b. $t=\frac{I}{Pr}$

## Exercises: Solve a Formula for a Specific Variable

Instructions: For questions 29-50, solve.

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

a. when $x=3$
b. in general

30. Solve the formula $5x+2y=10$ for $y$

a. when $x=4$
b. in general

Solution

a. $y=-5$
b. $y=\frac{10-5x}{2}$

31. Solve the formula $3x-y=7$ for $y$

a. when $x=-2$
b. in general

32. Solve the formula $4x+y=5$ for $y$

a. when $x=-3$
b. in general

Solution

a. $y=17$
b. $y=5-4x$

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

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

$a=90-b$

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

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

$c=180-a-b$

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

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

$y=13-9x$

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

40. Solve the formula $-5x+y=-1$ for $y$.
Solution

$y=-1+5x$

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

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

$y=\frac{11-3x}{4}$

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

44. Solve the formula $x-y=-3$ for $y$.
Solution

$y=3+x$

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

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

$W=\frac{P-2L}{2}$

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

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

$\pi =\frac{C}{d}$

49. Solve the formula $V=LWH$ for $L$.

50. Solve the formula $V=LWH$ for $H$.
Solution

$H=\frac{V}{LW}$

## Exercises: Everyday Math

Instructions: For questions 51-52, answer the given everyday math word problems.
51. Converting temperature. While on a tour in Greece, Tatyana saw that the temperature was $40^\circ$ Celsius. Solve for $F$ in the formula $C=\frac{5}{9}\left(F-32\right)$ to find the Fahrenheit temperature.

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

$10^\circ\;\mathrm{C}$

## Exercises: Writing Exercises

Instructions: For questions 53-54, answer the given writing exercises.

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

a. when $x=-3$
b. in general
c. Which solution is easier for you, a. or b.? Why?

54. Solve the equation $5x-2y=10$ for $x$

a. when $y=10$
b. in general
c. Which solution is easier for you, a. or b.? Why?

Solution