SOLUTION: A cubic shipping container had a volume of v3 cubic meters. The height of the container was decreased by a whole number of meters and the width was increased by a whole number of m

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A cubic shipping container had a volume of v3 cubic meters. The height of the container was decreased by a whole number of meters and the width was increased by a whole number of m      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 251549: A cubic shipping container had a volume of v3 cubic meters. The height of the container was decreased by a whole number of meters and the width was increased by a whole number of meters so that the volume of the container is now v3 + 2v2 – 3v. Find out the following:
a. By how many meters the height was decreased?
b. By how many meters the width was increased?

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
v[1] = v^3
v[2] = v^3 + 2v^2 - 3v

let a = amount height was decreased.
let b = amount width was increased.

v * (v-a) * (v+b) = v^3 + 2v^2 - 3v.

find the roots of v^3 + 2v^2 - 3v.

set the equation equal to 0 to get:

v^3 + 2v^2 - 3v = 0

factor out a v to get:

v * (v^2 + 2v - 3) = 0

factor v^2 + 2v - 3 to get:

(v-1) * (v+3) * v = 0

you get:

a = 1
b = 3

confirm by substituting in original equation to get:

v * (v-1) * (v+3) = (v^2 -v) * (v+3) = v^3 + 3v^2 -v^2 - 3v.

combine like terms to get:

v * (v-1) * (v+3) = v^3 + 2v^2 - 3v

since this is identical to the original equation of v^3 + 2v^2 - 3v, then the values for a and b are good.

v*v*v = v^3 = original equation for the cube.

v*(v-1)*(v+3) = v^3 + 2v^2 - 3v = original equation after taking 1 unit off the length and adding 3 units to the width.

answer is:

height was decreased by 1 unit.
width was increased by 3 units.