Question

Suppose that y varies directly with x and inversely with z; y = 27 when
x = 21, and z = 7. Write the equation that models the relationship. Then
find y when x = 25 and z = = 5.

Answer 1

The value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z

What is a proportional relationship?

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

We have:

y varies directly with x and inversely with z.

y ∝ x/z

Removing the proportional sign.

y = kx/z

k is the constant of proportionality.

Plug y = 27, x = 21, and z = 7 to get the value of k

27 = 21k/7

k = 9

y = 9x/z

Plug x = 25, and z = 5

y = 9(25)/5

y = 45

Thus, the value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z

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