Question

If y varies directly as z and inversely as x and y = –18 and z = 3 when x = 6, find y when x = 5 and z = –5.

36

18

9

64

Answer 1

y = 36

Explanation:

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

y =
`(kz)/(x)` ← k is the constant of variation

To find k use the condition y = - 18, z = 3 when x = 6 , then

- 18 =
`(3k)/(6)` ( multiply both sides by 6 )

- 108 = 3k ( divide both sides by 3 )

- 36 = k

y =
`(-36z)/(x)` ← equation of variation

When x = 5 and z = - 5, then

y =
`(-36(-5))/(5)` =
`(180)/(5)` = 36