# Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x = 25 and z = 5. How do you write the equation that models the relationship?

**Solution:**

Two quantities as said to follow a direct variation if both increase or decrease by the same factor.

If y varies jointly with x and inversely with z

y ∝ x

y ∝ 1/z

So the equation is

y = k x/z where k is the constant of variation

According to the statement

If y varies jointly with x and w and inversely with z

y = k wx/z …. (1)

It is given that

y = 400 when w = 10, x = 25 and z = 5

400 = k (10) (25)/5

400 = 250k/5

400 = 50k

Dividing both sides by 50

8 = k

So we get

y = 8 wx/z

Therefore, y = 8 wx/z is the equation that models the relationship.

## Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x = 25 and z = 5. How do you write the equation that models the relationship?

**Summary:**

Suppose that y varies jointly with w and x and inversely with z and y=400 when w=10, x=25 and z=5. y = 8 wx/z is the equation that models the relationship.

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