# 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.

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by moorejoy466

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

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'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

take the positive value. (take note that age can't be negative)

substitute x=20 to equation 1

y = x + 5

y = 20 + 5

therefore