SOLUTION: Rommie is 10 years older than Lady. In 10 years, the product of their ages is twice the product of their present ages. How old is Lady 5 years from now?

Question 1150476: Rommie is 10 years older than Lady. In 10 years, the product of their ages is twice the product of their present ages. How old is Lady 5 years from now?
Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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.

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

            How about this short solution ?

Let Lady's age be x years now. The Romnie's age is (x+10) years. In 10 years, Lady's age is (x+10) years and Rommie's age is ((x+10)+10) = (x+20) years. Next, the problem says 2x*(x+10) = (x+10)*(x+20). To solve it, first cancel the factor (x+10) in both sides 2x = x + 20. Then get the value of x x = 20. Thus Lady is 20 years old now. ANSWER. 5 years from now Lady will be 25 years old.

Solved.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Rommie is 10 years older than Lady. In 10 years, the product of their ages is twice the product of their present ages. How old is Lady 5 years from now?

NO WAY should this problem be that complex and "novel-like" as the other person makes it out to be.
CORRECT APPROACH:
Let Lady's current age be L
Then Rommie's is L + 10
Based on the given info., (L + 10)(L + 1O + 10) = 2L(L + 10)
(L + 10)(L + 20) = 2L(L + 10)
L + 20 = 2L ----- Factoring out GCF, L + 10
20 = 2L - L
20 = L, or Lady's current age
With Lady being 20, in 5 years, she'll be:
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