A. Solve the following showing the steps as indicated in the lesson.

1. If m varies directly as y and m is 6 when y is 36, find the constant of variation.

2. A varies directly as b. If A = 3 when b = 24, find b when A = 10.

3. If y varies inversely with x, and y = 5 when x = 8, what is k?

4. If y varies inversely with x and k = 0.32, what is x when y = 10?

5. B varies inversely as the square root of c. If b = 1 when c = 16, find b when c = 9.

6. Z varies inversely as the cube of d. If z = 3 when d = 2, find z when d is 4.

7. Using k as the constant of proportionality, write equation that expresses: Z varies jointly as x and y. If Z = 24 when x = 3 and y = 4, find Z when x = 5 and y = 6.

8. Using k as the constant, write equation that expresses: S varies jointly as b times the square of r.

B. Applications

9. There are about 200 calories in 50 grams of swiss cheese. Willie ate 70 grams of this cheese. About how many calories were in the cheese that he ate if the number of calories varies directly as the weight of the cheese?

10. The number of hours h that it takes m men to assemble x machines varies directly as the number of machines and inversely as the number of men. If four men can assemble 12 machines in four hours, how many men are needed to assemble 36 machines in eight hours?