Maths Quadratics problem

Question

Jenny is y^2 old and her daughter is y, when jenny is 13y, her daughter will be y^2. Find y

Answer 1

Present ages:

Jenny = y²

Daughter = y

 

Future ages:

Jenny = 13y

Daughter = y²

 

The key here, is to realize that at any point in time the difference in these two peoples ages will remain the same. Jenny will always be x years older than the daughter.

 

Present:

y²- y = x

 

Future:

13y - y² = x

 

Set them equal and solve for y

 

y² - y = 13y - y²

+y² both sides

2y² - y = 13y

-13y both sides

2y²- 14y = 0

factor/divide out 2

2(y²- 7y) = 0

0/2 = 0

y²- 7y = 0

factor/divide out y

y(y - 7) = 0

y = 0 (cannot be a solution since we are dealing with age)

y = 7