Math CentralQuandaries & Queries


Question from jessica, a student:

The story problem goes like this, it sounds like riddle more then anything,

Theresa is four years older than her younger sister Joni. Twelve years ago, she was twice
as old as her sister . Find the present age of the two siblings.

I came up with 32 and 28 I don't think this is correct how do I do it if this is not the correct answer

Hi Jessica.

12 years ago, Theresa would be 20 and Joni would be 16 and since 20 is not twice as old as 16, then your answers aren't right.

You can do this with algebra though:
Let J = Joni's present age and T = Theresa's present age.

Then T = J + 4 (that means Theresa is 4 years older than Joni today)
and (T - 12) = 2 (J - 12) (this means 12 years ago Theresa was twice as old as Joni was).

Well, we know T = J + 4, so we can substitute in (J + 4) wherever we see T (that's what equal means!)

So (T - 12) becomes ( (J+4) - 12). And the whole second equation is just

( (J+4) - 12) = 2 (J - 12).

Solve for J and use that to find T.
Stephen La Rocque.

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