constant variation

Question

If y varies directly as x and y = 72 when x = 27, find y when x = 24

Answer 1

When we say y varies directly with x then we are saying y = kx where "k" is a constant depending on the specific problem. To find the value of "k", we need a data point (an x and a y). In this case they gave us the information that "y = 72 when x = 27" so we can say:

y = kx

72 = k•27

k = 72/27 = 8/3

So now we can write the specific equation for this problem. It is:

y = 8/3x

Now we can find y when x = 24:

y = 8/3•24 = 64