Question 1150476
let x = rommie's age now.
let y = lady's age now.
you get:
x = y + 10


in 10 years, the product of their ages is twice the product of their ages now.
you get:
(x + 10) * (y + 10) = 2 * x * y
simplify this equation to get:
x * y + x * 10 + 10 * y + 10 * 10 = 2 * x * y
since x = y + 10, replace x with that to get:
(y + 10) * y + (y + 10) * 10 + 10 * y + 10 * 10 = 2 * (y + 10) * y
simplify further to get:
y^2 + 10 * y + 10 * y + 100 + 10 * y + 100 = 2 * (y^2 + 10 * y)
simplify further to get:
y^2 + 10 * y + 10 * y + 100 + 10 * y + 100 = 2 * y^2 + 20 * y
combine like terms to ge:
y^2 + 30 * y + 200 = 2 * y^2 + 20 * y
subtract (2 * y^2 + 20 * y) from both sides of the equation to get:
y^2 + 30 * y + 200 - 2 * y^2 - 20 * y = 0
combine like terms to get:
-y^2 + 10 * y + 200 = 0
multiply both sides of this equation by -1 to get:
y^2 - 10 * y - 200 = 0
factor this equation to get:
(y - 20) * (y + 10) = 0
solve for y to get:
y = 20 or y = -10
solution has to be positive, so any possible solution is:
y = 20


since x = y + 10, then x = 30
you have x = 30 and y = 20
that means that rommie's current age is 30 and lady's current age is 20.
in 10 years, rommie will be 40 and lady will be 30.
the product of their current ages is 30 * 20 = 600
the product of their ages 10 years from now is 40 * 30 = 1200
1200 = 2 * 600, confirming that the requirements of the problem have been verified as true when rommie's current age (represented by the value of x) is 30 and lady's current age (represented by y) is 20.


lady is 20 years old now.
in 5 years, she will be 25.
that's your solution.