Math problem, please help?

Question

An open bin with a square bottom, rectangular sides and a height of 3 m is to be constructed using all of $630 worth material. The material for the bottom costs $54 per square meter and the material for the side costs $24 per square meter. What is the volume of this bin?

Answer 1

Suppose the base square has side x meters. So x>0 and x^2 is the area of the bottom and 4(3)x  is the lateral area.

So 54x^2 - 24(12x) = 630.

Divide by 18,

3x^2  - 16 x - 35 =0 can you solve this now?

(x-7)(3x+5) = 0

But x>0 so x = 7.

Vol = 7(7)(3) = 147 m^3