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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?

  • math -

    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

  • math -

    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.

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