Hello Toby,

If one variable is directly proportional to another (say **z is directly proportional to x**), then

z = kx

where k is a constant (the constant of proportionality.)

On the other, when **z is inversely proportional to x**, we can write

z = C/x

where C is a constant. In your problem, z depends on both x and y, and we are told that z is directly proportional to x and inversely proportional to y. We can express this relationship as

**z = Kx/y**

for some constant K.

Now to solve your problem, **we must first find the constant K**. We use that fact that if x = 14 and y = 10, then z = 26.6

26.6 = (K·14)/10

26.6 = 1.4K

so

K = 26.6/1.4

**K = 19**

Now we have **z = 19x/y**, and we can find the value of z when x = 24 and y = 15.

z = (19·24)/15

**z = 30.4**

Hope that helps! Let me know if you need any more help.

William