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.

Answer 1

Answer:

y = 36

Step-by-step explanation:

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

y = $\frac{kz}{x}$ ← k is the constant of variation

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

- 18 = $\frac{3k}{6}$ ( multiply both sides by 6 )

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

- 36 = k

y = $\frac{-36z}{x}$ ← equation of variation

When x = 5 and z = - 5, then

y = $\frac{-36(-5)}{5}$ = $\frac{180}{5}$ = 36