SOLUTION: Mary Lou is 4 years younger than her sister, Jane. Their mother, who is a mathematics teacher, noticed that the product of the ages of the two sisters is 32. How old are the girls?

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Question 697142: Mary Lou is 4 years younger than her sister, Jane. Their mother, who is a mathematics teacher, noticed that the product of the ages of the two sisters is 32. How old are the girls?
So far i have : y= age of jane
x= age of mary lu
y-x
y(x)=32
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, you are on the right track but the trick is that there are two equations.
Given:
Y = Age of Jane
X = Age of Mary Lou
-----------------
Setup:
Equation 1: Y+=+X+%2B+4
Equation 2: Y+%2A+X+=+32
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Since equation 1 is already solved for Y, plug (X + 4) into equation 2 for Y.
Equation 2: Y+%2A+X+=+32
%28X+%2B+4%29%2AX+=+32
Simplify
X%5E2+%2B+4X+=+32
Subtract 32 from both sides to set the equation equal to zero
X%5E2+%2B+4X+-+32+=+0
You can now factor the equation or use the quadratic equation.
Here is the quadratic equation approach.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aX%5E2%2BbX%2Bc=0 (in our case 1X%5E2%2B4X%2B-32+=+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=%284%29%5E2-4%2A1%2A-32=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+144+%29%29%2F2%5Ca.

X%5B1%5D+=+%28-%284%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+4
X%5B2%5D+=+%28-%284%29-sqrt%28+144+%29%29%2F2%5C1+=+-8

Quadratic expression 1X%5E2%2B4X%2B-32 can be factored:
1X%5E2%2B4X%2B-32+=+1%28X-4%29%2A%28X--8%29
Again, the answer is: 4, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-32+%29

So X is 4 or -8.
Since age is a positive number this means that Mary Lou is 4
Now plug 4 into equation 1 for X to solve for Jane's age
Equation 1: Y+=+X+%2B+4
Y+=+%284%29+%2B+4
highlight%28Y+=+8%29