SOLUTION: A mother is three times as old as her daughter. Four years ago the product of their ages was 256. Find their current ages. Would the equation be (3x-4)(x-4)=256?

Question 852410: A mother is three times as old as her daughter. Four years ago the product of their ages was 256. Find their current ages. Would the equation be (3x-4)(x-4)=256?
Answer by pmesler(52) (Show Source): You can put this solution on YOUR website!
Let the daughter's age = x
Let the mother's age = 3x

The product of their ages is 256. In other words
(3x-4)(x-4) = 256
Use FOIL to simplify.
3x^2-16x+16 = 256
Subtract 256 from both sides to make this a quadratic equation.

3x^2-16x-240 = 0
Solve for x using the quadratic equation.

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=3136 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 12, -6.66666666666667. Here's your graph:

From this you can see that x = (-6.66,0) and x = (12,0). Obviously we can disregard x = -6.66 since you can't have a negative age. That means that the daughter is 12 years old and her mother is 36 years old.

Let's plug in these values of x to see if the original equation checks out.
(3(12)-4)(12-4) = 256
32 * 8 = 256
It checks out so those are the correct ages.

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