Question

The variable z is directly proportional to x, and inversely proportional to y. When x is 16 and y is 5, z has the value 16. What is the value of z when x= 21, and y= 14 Round to at least the thousandths place if needed.

Answer 1

z = 7.5

Explanation:

Given that 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 when x = 16, y = 5, z = 16, then

k =
`(zy)/(x)` =
`(16(5))/(16)` = 5

z =
`(5x)/(y)` ← equation of proportionality

When x = 21, y = 14, then

z =
`(5(21))/(14)` = 7.5