# Ana is 5 years older than Beth. In 5 years, the product of their ages is 1.5 times the product of their present ages. How old is Beth now?

1
by moorejoy466
I know it's 5 but I forgot how to solve it haha.

2014-11-07T00:26:36+08:00
Let 'x' be the age of Beth at present
'y' be the age of Ana at present
since Ana is 5 years older than Beth then you will have the equation as:
y = x + 5   ----equation 1
in five years, their ages would be:
Beth:  x+5
Ana:  y+5
given the statement that the product of their ages in 5 years will be 1.5 fold as the product of their ages at present, you will have the equation as:
product of ages 5yrs from now = 1.5 of product of ages at present
(x+5)(y+5) = 1.5(x)(y)   ----equation 2
substitute equation 1 to equation 2
(x+5)(y+5) = 1.5(x)(y)
(x+5)(x+5+5) = 1.5x(x+5)
(x+5)(x+10) = 1.5x(x+5)
use FOIL method
x² + 10x + 5x + 50 = 1.5x² + 7.5x
transposing everything to the right side you'll have:
0 = 1.5x² - x² + 7.5x -10x - 5x - 50
or you'll have it as:
1.5x² - x² + 7.5x -10x - 5x - 50 = 0
combine like terms
0.5x² - 7.5x - 50 = 0
multiply the whole equation with 2
[0.5x² - 7.5x - 50 = 0]  x2
x² - 15x - 100 = 0
factor
x² - 15x - 100 = 0
(x - 20)(x+5) = 0
x = 20, x = -5
take the positive value. (take note that age can't be negative)
substitute x=20 to equation 1
y = x + 5
y = 20 + 5
y = 25
therefore Beth is 20 yrs old at present and Ana is 25 yrs old.