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 [latex]8\frac{1}{2}[/latex] hours at [latex]72[/latex] miles per hour. How much distance did he travel?
2. Socorro drove for [latex]4\frac{5}{6}[/latex] hours at [latex]60[/latex] miles per hour. How much distance did she travel?
Solution

[latex]290[/latex] miles

3. Yuki walked for [latex]1\frac{3}{4}[/latex] hours at [latex]4[/latex] miles per hour. How far did she walk?
4. Francie rode her bike for [latex]2\frac{1}{2}[/latex] hours at [latex]12[/latex] miles per hour. How far did she ride?
Solution

[latex]30[/latex] miles

5. Connor wants to drive from Tucson to the Grand Canyon, a distance of [latex]338[/latex] miles. If he drives at a steady rate of [latex]52[/latex] 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 [latex]380[/latex] miles and the bus travels at a steady rate of [latex]76[/latex] miles per hour. How long will the bus ride be?
Solution

[latex]5[/latex] hours

7. Aurelia is driving from Miami to Orlando at a rate of [latex]65[/latex] miles per hour. The distance is [latex]235[/latex] 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 [latex]180[/latex] miles. If he rides at a steady rate of [latex]16[/latex] miles per hour, how many hours will the trip take?
Solution

[latex]11.25[/latex] hours

9. Javier is driving to Bangor, [latex]240[/latex] miles away. If he needs to be in Bangor in [latex]4[/latex] hours, at what rate does he need to drive?
10. Alejandra is driving to Cincinnati, [latex]450[/latex] miles away. If she wants to be there in [latex]6[/latex] hours, at what rate does she need to drive?
Solution

[latex]75[/latex] mph

11. Aisha took the train from Spokane to Seattle. The distance is [latex]280[/latex] miles and the trip took [latex]3.5[/latex] hours. What was the speed of the train?
12. Philip got a ride with a friend from Denver to Las Vegas, a distance of [latex]750[/latex] miles. If the trip took [latex]10[/latex] hours, how fast was the friend driving?
Solution

[latex]75[/latex] mph

Exercises: Solve a Formula for a Specific Variable

Instructions: For questions 13-20, use the formula [latex]d=rt[/latex].

13. Solve for [latex]t[/latex]

a. when [latex]d=350[/latex] and [latex]r=70[/latex]
b. in general

14. Solve for [latex]t[/latex]

a. when [latex]d=240[/latex] and [latex]r=60[/latex]
b. in general

Solution

a. [latex]t=4[/latex]
b. [latex]t=\frac{d}{r}[/latex]

15. Solve for [latex]t[/latex]

a. when [latex]d=510[/latex] and [latex]r=60[/latex]
b. in general

16. Solve for [latex]t[/latex]

a. when [latex]d=175[/latex] and [latex]r=50[/latex]
b. in general

Solution

a. [latex]t=3.5[/latex]
b. [latex]t=\frac{d}{r}[/latex]

17. Solve for [latex]r[/latex]

a. when [latex]d=204[/latex] and [latex]t=3[/latex]
b. in general

18. Solve for [latex]r[/latex]

a. when [latex]d=420[/latex] and [latex]t=6[/latex]
b. in general

Solution

a. [latex]r=70[/latex]
b. [latex]r=\frac{d}{t}[/latex]

19. Solve for [latex]r[/latex]

a. when [latex]d=160[/latex] and [latex]t=2.5[/latex]
b. in general

20. Solve for [latex]r[/latex]

a. when [latex]d=180[/latex] and [latex]t=4.5[/latex]
b. in general

Solution

a. [latex]r=40[/latex]
b. [latex]r=\frac{d}{t}[/latex]

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

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

21. Solve for [latex]b[/latex]

a. when [latex]A=126[/latex] and [latex]h=18[/latex]
b. in general

22. Solve for [latex]h[/latex]

a. when [latex]A=176[/latex] and [latex]b=22[/latex]
b. in general

Solution

a. [latex]h=16[/latex]
b. [latex]h=\frac{2A}{b}[/latex]

23. Solve for [latex]h[/latex]

a. when [latex]A=375[/latex] and [latex]b=25[/latex]
b. in general


24. Solve for [latex]b[/latex]

a. when [latex]A=65[/latex] and [latex]h=13[/latex]
b. in general

Solution

a. [latex]b=10[/latex]
b. [latex]b=\frac{2A}{h}[/latex]

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

Instructions: For questions 25-28, use the formula [latex]I=Prt[/latex]

25. Solve for the principal, [latex]P[/latex] for

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

26. Solve for the principal, [latex]P[/latex] for

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

Solution

a. [latex]P=$13,166.67[/latex]
b. [latex]P=\frac{I}{rt}[/latex]

27. Solve for the time, [latex]t[/latex] for

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

28. Solve for the time, [latex]t[/latex] for

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

Solution

a. [latex]t=2[/latex] years
b. [latex]t=\frac{I}{Pr}[/latex]

Exercises: Solve a Formula for a Specific Variable

Instructions: For questions 29-50, solve.

29. Solve the formula [latex]2x+3y=12[/latex] for [latex]y[/latex]

a. when [latex]x=3[/latex]
b. in general

30. Solve the formula [latex]5x+2y=10[/latex] for [latex]y[/latex]

a. when [latex]x=4[/latex]
b. in general

Solution

a. [latex]y=-5[/latex]
b. [latex]y=\frac{10-5x}{2}[/latex]

31. Solve the formula [latex]3x-y=7[/latex] for [latex]y[/latex]

a. when [latex]x=-2[/latex]
b. in general

32. Solve the formula [latex]4x+y=5[/latex] for [latex]y[/latex]

a. when [latex]x=-3[/latex]
b. in general

Solution

a. [latex]y=17[/latex]
b. [latex]y=5-4x[/latex]

33. Solve [latex]a+b=90[/latex] for [latex]b[/latex].
34. Solve [latex]a+b=90[/latex] for [latex]a[/latex].
Solution

[latex]a=90-b[/latex]

35. Solve [latex]180=a+b+c[/latex] for [latex]a[/latex].
36. Solve [latex]180=a+b+c[/latex] for [latex]c[/latex].
Solution

[latex]c=180-a-b[/latex]

37. Solve the formula [latex]8x+y=15[/latex] for [latex]y[/latex].
38. Solve the formula [latex]9x+y=13[/latex] for [latex]y[/latex].
Solution

[latex]y=13-9x[/latex]

39. Solve the formula [latex]-4x+y=-6[/latex] for [latex]y[/latex].
40. Solve the formula [latex]-5x+y=-1[/latex] for [latex]y[/latex].
Solution

[latex]y=-1+5x[/latex]

41. Solve the formula [latex]4x+3y=7[/latex] for [latex]y[/latex].
42. Solve the formula [latex]3x+2y=11[/latex] for [latex]y[/latex].
Solution

[latex]y=\frac{11-3x}{4}[/latex]

43. Solve the formula [latex]x-y=-4[/latex] for [latex]y[/latex].
44. Solve the formula [latex]x-y=-3[/latex] for [latex]y[/latex].
Solution

[latex]y=3+x[/latex]

45. Solve the formula [latex]P=2L+2W[/latex] for [latex]L[/latex].
46. Solve the formula [latex]P=2L+2W[/latex] for [latex]W[/latex].
Solution

[latex]W=\frac{P-2L}{2}[/latex]

47. Solve the formula [latex]C=\pi d[/latex] for [latex]d[/latex].
48. Solve the formula [latex]C=\pi d[/latex] for [latex]\pi[/latex].
Solution

[latex]\pi =\frac{C}{d}[/latex]

49. Solve the formula [latex]V=LWH[/latex] for [latex]L[/latex].

50. Solve the formula [latex]V=LWH[/latex] for [latex]H[/latex].
Solution

[latex]H=\frac{V}{LW}[/latex]

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 [latex]40^\circ[/latex] Celsius. Solve for [latex]F[/latex] in the formula [latex]C=\frac{5}{9}\left(F-32\right)[/latex] 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 [latex]50^\circ[/latex] Fahrenheit. Solve for [latex]C[/latex] in the formula [latex]F=\frac{9}{5}C+32[/latex] to find the Celsius temperature.
Solution

[latex]10^\circ\;\mathrm{C}[/latex]

Exercises: Writing Exercises

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

53. Solve the equation [latex]2x+3y=6[/latex] for [latex]y[/latex]

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

54. Solve the equation [latex]5x-2y=10[/latex] for [latex]x[/latex]

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

Solution

Answers will vary.

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Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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