The dimensions of a fish tank are x-3, x-4, and x-2. The fish tank has a volume of 23x+3 cubic units. Solve for x, and find the dimensions of the fish tank.

Question

I wrote the polynomial equation for the volume, and got x³ - 9x² + 26x - 24, i'd also like to know if that's correct if possible.

Answer 1

V - volume of fish tank

V = (x - 2)(x - 3)(x - 4) =

(x² - 5x + 6)(x - 4) =

x³ - 9x² + 26x - 24

I’ve checked your solution. You got it right!

Good job!

x³ - 9x² + 26x - 24 = 23x + 3

x³ - 9x² + 3x - 27 = 0

x²(x - 9) + 3(x - 9) = 0

(x - 9)(x² + 3) = 0

x = 9

(Note that x² + 3 = 0 → x² = -3 → no real solutions)

Answer 2

Hello, Michael,

I also get x³ - 9x² + 26x - 24 for the volume. That is equal to 23x + 3 in³ .

x³ - 9x² + 26x - 24 = 23x + 3

x³ - 9x² + 3x - 24 = 3

x³ - 9x² + 3x - 27 = 0

I believe x=9 in would work for this function.

Bob