Suppose that y varies directly with x and inversely with z, and y = 18 when x = 15 and z = 5. Write the equation that models the relationship. Then find y when x = 21 and z = 7.
To write the equation that models the relationship, we can use the formula for direct and inverse variation:
y = kx/z
where k is the constant of proportionality.
Using the values given when x = 15, y = 18, and z = 5:
18 = k * 15 / 5
18 = 3k
k = 6
Therefore, the equation that models the relationship is:
y = 6x/z
Now, we can find y when x = 21 and z = 7:
y = 6 * 21 / 7
y = 126 / 7
y = 18
So, when x = 21 and z = 7, y = 18.