Algebra Question?

Question

I was wondering if anyone could help me out with this question, I really don't get what I'm supposed to do.

x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and tare doubled?

Answer 1

"x varies directly as the square of s": this means that x is proportional to s^2.
"x varies inversely as t": this means that x is proportional to 1/t.
Combining these means that x is some constant multiplied by s^2/t. Let x = k.s^2/t.

When s is doubled, we replace s by 2s to get k.(2s)^2/t = 4ks^2/t = 4x. So the new value of x is four times the old value.

When s and t are both doubled, we get k.(2s)^2/(2t) = 2ks^2/t = 2x. So the new value of x is twice the old value.