SOLUTION: An open box is made from a piece of cardboard 15 inches by 22 inches by cutting out squares from each corner. If the resulting bas has area of 110in(squared), what is the length of

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: An open box is made from a piece of cardboard 15 inches by 22 inches by cutting out squares from each corner. If the resulting bas has area of 110in(squared), what is the length of      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 188520: An open box is made from a piece of cardboard 15 inches by 22 inches by cutting out squares from each corner. If the resulting bas has area of 110in(squared), what is the length of the sides of the squares?
a) Draw and label a picture
b) Find the length of the squares
**************************************************************************
I've been trying to help my son who is in 11th grade, but I can't. The closest he came to coming to a solution is:
330-30x-44x+4x(squared)=110in(squared)
(sorry I don't know where the "squared" character is on my keyboard
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An open box is made from a piece of cardboard 15 inches by 22 inches by cutting out squares from each corner. If the resulting bas has area of 110in(squared), what is the length of the sides of the squares?
a) Draw and label a picture
b) Find the length of the squares
------------------------
When the squares are cut out, the bottom will be (15-2x)*(22-2x) = 110
4x^2 - 74x + 330 = 110
4x^2 - 74x + 220 = 0
2x^2 - 37x + 110 = 0
x^2 - 18.5x + 55 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-18.5x%2B55+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-18.5%29%5E2-4%2A1%2A55=122.25.

Discriminant d=122.25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18.5%2B-sqrt%28+122.25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18.5%29%2Bsqrt%28+122.25+%29%29%2F2%5C1+=+14.778336096874
x%5B2%5D+=+%28-%28-18.5%29-sqrt%28+122.25+%29%29%2F2%5C1+=+3.721663903126

Quadratic expression 1x%5E2%2B-18.5x%2B55 can be factored:
1x%5E2%2B-18.5x%2B55+=+%28x-14.778336096874%29%2A%28x-3.721663903126%29
Again, the answer is: 14.778336096874, 3.721663903126. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18.5%2Ax%2B55+%29

The sides of the squares cut out = 3.72166... inches