I need help with algebra 2 Problems?

jasmine is a manufacturing engineer who is trying to find out if she can use a 12-inch by 20-inch sheet of cardboard and a 15-inch by 16-inch sheet of cardboard to make boxes with the same height and volume. Is such a pair of boxes possible?

Also,
A store is offering a discount of thirty percent on a suit. There is a sales tax of six percent.
A) using a composition of functions, represent the situation in which the discount is taken before the sales tax is applied.
B) Using a composition of functions, represent the situation in which the sales tax is applied beofre the discount is taken.
C) Compare the composite functions from parts A and B. Does one of them result in a lower final cost? Explain.

So I think A is (x * 0.7) = y then (y * 0.94)
I got the 0.7 from 30% because x * 0.7 is the same as x * 0.3 = y, x – y = final answer. For example, if x was 15: 15 * 0.7 = 10.5 which is the same as 15 * 0.3 = 4.5, 15 – 4.5 = 10.5

Then, I think B is (x * 0.94)= y, then (y * 0.7)
So C would be that they would have the same price? Right?

Thanks !

For A,B and C,, discount is f(x) = 0.7x as you said. But tax is g(x) = 1.06x because you add the tax to the 100% price.

So for A you do the discount first so it’s listed second: g(f(x)) = g(0.7x) = 1.06(0.7x)
B is f(g(x)) = f(1.06x) = 0.7(1.06x)
and by commutative property they are the same

On the other, you make the boxes by cutting squares out of each corner then folding up the flaps.

If x = the length of a side of the square, that makes each side be 2x shorter, so you’d get this equation for volumes:

x (12 – 2x)(20 – 2x) = x(15 – 2x)(16 – 2x)

divide both sides by x: (12 – 2x)(20 – 2x) = (15 – 2x)(16 – 2x)
multiplied out that is 240 – 64x + 4x^2 = 240 – 62x + 4x^2

subtract 240 and 4x^2, and add 64x to both sides and you get just 0x = 2x meaning x = 0
so no, you can’t make the boxes the same