Question

Suppose f varies directly as g, and f varies inversely as h. Find g when f = 12 and h = 10, if g = 198 when h = –11 and f = –6. Round your answer to the nearest hundredth, if necessary.

Question 5 options:

–360

–40

40

360

Answer 1

360

Explanation:

f varies directly as g

f = kg where k is the constant of variation

f varies inversely as h

f = kg/h

We know g = 198 when h = –11 and f = –6. Substituting in

-6 = k*198/(-11)

-6 =k*(-18)

Dividing each side by -18

-6/-18 = k*-18/-18

1/3 =k

Our equation is

f = 1/3 g/h

Letting f = 12 and h = 10

12 = 1/3 g/10

Multiply each side by 10

12*10 =1/3 g/10*10

120 = 1/3 g

Multiply each side by 3

120*3 =1/3 g *3

360 =g