SOLUTION: a woman is 4 times older than her daughter, 6 years ago the product of their ages was 136. find their present age

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Question 627671: a woman is 4 times older than her daughter, 6 years ago the product of their ages was 136. find their present age
Found 2 solutions by ewatrrr, Maths68:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

a woman is 4 times older than her daughter's agehighlight%28x%29 , 

6 years ago the product of their ages was 136.

Question states***  6 years ago...

 (x-6)(4x-6) = 136

  4x^2 -30x + 36 = 136

  4x^2 -30x - 100 = 0

  2x^2 - 15x - 50 = 0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%2815+%2B-+sqrt%28625+%29%29%2F%284%29+

x+=+%2815+%2B-+25%29%2F%284%29+

    x = 10,  throwing out the negative solution for age

 daughter is 10 and her mother is 40   4%2A10



and... 6 years ago...checking our answer

 4%2A34+=+136

Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let
Present age of woman = w years old
Present age of daughter = d years old

woman is 4 times older than her daughter
w=4d............(1)
6 years ago
woman was = w-6 years old
daughter was = d-6
then
product of their ages was 136
(w-6)(d-6)=136
substitute the value of from (1) to above equation
(4d-6)(d-6)=136
4d^2-24d-6d+36=136
4d^2-30d+36=136
2(2d^2-15d+18)=136
Divide by 2 both sides
2(2d^2-15d+18)/2=136/2
2d^2-15d+18=68
2d^2-15d+18-68=0
2d^2-15d-50=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ad%5E2%2Bbd%2Bc=0 (in our case 2d%5E2%2B-15d%2B-50+=+0) has the following solutons:

d%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=%28-15%29%5E2-4%2A2%2A-50=625.

Discriminant d=625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--15%2B-sqrt%28+625+%29%29%2F2%5Ca.

d%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+625+%29%29%2F2%5C2+=+10
d%5B2%5D+=+%28-%28-15%29-sqrt%28+625+%29%29%2F2%5C2+=+-2.5

Quadratic expression 2d%5E2%2B-15d%2B-50 can be factored:
2d%5E2%2B-15d%2B-50+=+2%28d-10%29%2A%28d--2.5%29
Again, the answer is: 10, -2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-15%2Ax%2B-50+%29

d=10 or d=-2.5 (unacceptable)
so
d=10
Put the value of d in (1)
w=4d
w=4(10)
w=40

Present age of woman = w = 40 years old
Present age of daughter = d = 10 years old