Question

The variable z is directly proportional to x, and inversely proportional to y. When x is 7 and y is 7, z has the value 2. What is the value of z when x= 10, and y= 12

Answer 1

z =
`(5)/(3)`

Explanation:

Given z is directly proportional to x and inversely proportional to y then the equation relating them is

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

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

k =
`(zy)/(x)` =
`(2(7))/(7)` = 2

z =
`(2x)/(y)` ← equation of proportionality

When x = 10 and y = 12, then

z =
`(2(10))/(12)` =
`(20)/(12)` =
`(5)/(3)`