Question 344344
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 {{{highlight_green(24)}}} years-old, and S, or Sally is (42 – 24), or {{{highlight_green(18)}}} 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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