Question

If y varies directly as x and inversely as z and y = 4 when x = 2 and z = 7, find y when x =

6 and z = 3.

Answer 1

y = 28

Explanation:

Given that y varies directly as x and inversely as z then the equation relating them is

y =
`(kx)/(z)` ← k is the constant of variation

To find k use the condition y = 4 when x = 2 and z = 7, then

4 =
`(2k)/(7)` ( multiply both sides by 7 )

28 = 2k ( divide both sides by 2 )

14 = k

y =
`(14x)/(z)` ← equation of variation

When x = 6 and z = 3 , then

y =
`(14(6))/(3)` = 14 × 2 = 28