SOLUTION: Marivic is five years older than Michelle. In three years, the product of her age and Michelle's age five years ago will be 90 years. Find their present ages.

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Question 74272: Marivic is five years older than Michelle. In three years, the product of her age and Michelle's age five years ago will be 90 years. Find their present ages.
Answer by vidhyak(98) (Show Source):
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Let Marivic's age be x
Let Michelle's age be y

Marivic is five years older than Michelle
x = y + 5 -----------------------eq. 1

In three years, the product of her age and Michelle's age five years ago will be 90 years
In three years marvic will be x + 3 yrs old
Michelle's age five years ago was y - 5 yrs old

(x + 3)(y - 5) = 90 --------------eq 2

Substitue eq1 in eq2
(y + 5 + 3) (y - 5) = 90
(y + 8) (y - 5) = 90
y^2 + 3y -40 = 90
y^2 + 3y -130 = 0

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=529 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10, -13. Here's your graph:

Answers for y= 10,-13
Age is a positive integer, so Michelle's age is 10

x = y + 5
x= 15
so Marivic's age is 15