Question

Suppose f varies directly as g, and f varies inversely as h.

f = -12 when h = 4 and g = -3.
Find g when f = 28 and h = 8.

Answer 1

g = 14

Explanation:

Given that f varies directly as g and inversely as h then the equation relating them is

f =
`(kg)/(h)` ← k is the constant of variation

To find k use the condition f = - 12 when h = 4 and g = - 3, that is

- 12 =
`(-3k)/(4)` ( multiply both sides by 4 )

- 48 = - 3k ( divide both sides by - 3 )

16 = k

f =
`(16g)/(h)` ← equation of variation

When f = 28 and h = 8 , then

28 =
`(16g)/(8)` = 2g ( divide both sides by 2 )

g = 14