Question 852410
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. *[invoke quadratic "x", 3, -16, -240 ]



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.