Suppose that y varies directly with x and inversely with z, y = 18 when x = 15 and z = 5. How do you write the equation that models the relationship, then find y when x = 21 and z = 7?

Solution:

Given, y ∝ x/z

To convert to an equation multiply by a constant k.

y = kx/z

Next, find the value of k using the given condition.

i.e. y = 18, x = 15, z = 5.

18 = k(15/5)

18 = k(3)

k= 6

The equation becomes y = 6x/z

When x = 21, z = 7,

y = (6)(21)/(7)

y = (6)(3)

y = 18

Therefore, the equation is y = 6x/z and its value at x = 21 and z = 7 is 18.

---

Suppose that y varies directly with x and inversely with z, y = 18 when x = 15 and z = 5. How do you write the equation that models the relationship, then find y when x = 21 and z = 7?

Summary:

Suppose that y varies directly with x and inversely with z, y = 18 when x = 15 and z = 5. The equation that models the relationship is y = 6x/z. The value y when x = 21 and z = 7 is 18.