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?

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) (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:
Equation 2:
------------------
Since equation 1 is already solved for Y, plug (X + 4) into equation 2 for Y.
Equation 2:

Simplify

Subtract 32 from both sides to set the equation equal to zero

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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=144 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, -8. Here's your graph:

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:

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