SOLUTION: The volume of a rectangular tank is 14 ft less than twice the volume of a cube. The length of the tank is 1 foot more than the length of an edge of the cube, its width is 1 foot

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The volume of a rectangular tank is 14 ft less than twice the volume of a cube. The length of the tank is 1 foot more than the length of an edge of the cube, its width is 1 foot       Log On


   

Question 1186811: The volume of a rectangular tank is 14 ft less than twice the volume of a cube. The length of the tank is 1 foot more than the length of an edge
of the cube, its width is 1 foot less than the length of an edge of the
cube, and its height is 2 feet greater than the length of an edge of the
cube. What are the dimensions of the cube and of the tank​?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
c, the edge length of the cube
Rectangular Tank Length, c+1
Tank width, c-1
Tank height, c+2
Cube's volume, c^3

Volume of tank is 14 CUBIC ft. less than twice that of the cube.
2c%5E3-14=%28c%2B1%29%28c-1%29%28c%2B2%29
Simplify and solve this for c, first.
--

2c%5E3-14=%28c%5E2-1%29%28c%2B2%29
2c%5E3-14=c%5E3-c%2B2c%5E2-2
c%5E3-2c%5E2%2Bc-12=0
-
c%5E3-2c%5E2%2Bc=12
c%28c%5E2-2c%2B1%29=12
highlight_green%28c%28c-1%29%5E2=12%29

Basic multiplication facts may be enough to find c.

If c is 3, then
3%283-1%29%283-1%29
3%2A2%2A2
12-----------same as the right-hand side of the simplified equation.

c, edge length of the cube is 3.