Question

Dorthy is 6 years older than Ricardo. The product of their present age is twice what the product of their ages was 6 years ago. How old is Dorthy?

Answer 1

Ricardo's present age --- x
Dorothy's present age --- x+6

product of their present ages = x(x+6)

6 years ago:
Ricardo x-6
Dorothy x
product of their ages then = x(x-6)

x(x+6) = 2x(x-6)
solve for x, sub into x+6

Answer 2

Let D=age of Dorthy.

" Dorthy is 6 years older than Ricardo. "
Age of Ricardo = D-6

"The product of their present age"
D(D-6)

"is twice what the product of their ages was 6 years ago"
=2*((D-6)*(D-6-6))

Thus
D(D-6) = 2*((D-6)*(D-12))

Simplify and solve for D and reject the solution of D=6 because it is a trivial solution. Check the answer by substitution into problem data.