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bill is 2 years older than ted. in 5 years, 5 times ted's age will be 4 times bill's age. how old is ted?

  • math -

    bill is 2 years older than ted. in 5 years, 5 times ted's age will be 4 times bill's age. how old is ted?

    B = T + 2
    4(B + 2) = 5(T + 2)

    Can you take it from here.

  • math -

    let x=Bill's age, y=Ted's age

    Bill is two years older than Ted. This gives the first equation:
    y=x-2

    In 5 years, their ages will be:
    Bill=(x+5), Ted=(y+5)

    and...
    4*Bill's age=5*Ted's age
    4*(x+5)=5*(y+5)

    Use the first equation to substitute for y in the second equation. Then, you will only have x's. Solve for x. Plug the solved value for x into the first equation to easily find y.

  • math -

    Bill is 2 years older than ted
    (1) b = t + 2
    where b = bill's age TODAY and t = ted's age TODAY

    In 5 years 5 times ted's age will be 4 times bill's age:

    (2) 5(t+5) = 4(b+5)

    Put equation (1) into (2) for b.

    5(t+5) = 4(t+2+5) ==> 5t+25 = 4t+28
    solve for t to get t = 3

    So ted is 3 and bill is 5 years old.

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