Question 344344: when you add up harry's age and sally's age the total is 42. harry is twice as old as sally was at the time when he was as old as sally is now. how old are they?
Answer by MathTherapy(10551)   (Show Source):
You can put this solution on YOUR website! Let Harry’s and Sally’s current ages be H and S, respectively
Since Harry and Sally’s current ages sum to 42, then Harry is now (42 – S) years-old and Sally is (42 – H) years-old, because H + S = 42
Furthermore, since Harry is older that Sally, their difference in ages is H - S
Sally’s current age, 42 – H is the age that Harry was (H – S) years ago, at which time Sally was 42 – H – (H – S), or (42 – H – H + S), or (42 – 2H + S) years-old
Now, since Harry’s current age, 42 – S was twice Sally’s age at the time Harry was Sally’s current age, we’ll then have:
42 – S = 2(42 – 2H + S)________42 – S = 84 – 4H + 2S________4H - 3S = 42
We now have:
H + S = 42 --------- eq (i)
4H – 3S = 42 ------ eq (ii)
3H + 3S = 126 ----- eq(iii)_______Multiplying eq (i) by 3
7H = 168________Adding eq (ii) & (iii)
H = 24
Therefore, H, or Harry is currently  years-old, and S, or Sally is (42 – 24), or  years-old.
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Check
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Harry is currently 24 and Sally 18
Differences in their ages = 6 (24 - 18)
6 years ago, Harry was Sally's current age, 18, and Sally was 12 (18 - 6) then
This makes Harry's current age, 24 twice that of Sally's age of 12 years, 6 years ago (24 = 2*12).
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