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.