SOLUTION: One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

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Question 112768: One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write an expression for each phrase
:
Let x = H's age now
;
One-half of Heather's age two years from now
1%2F2(x+2)
:
plus one-third of her age three years ago
+ 1%2F3(x-3)
is twenty years. How old is she now?
:
Put it all together, ("is" usually means "="
1%2F2(x+2) + 1%2F3(x-3) = 20
:
Get rid of those annoying denominators, multiply equation 6, resulting in:
3(x+2) + 2(x-3) = 6(20)
:
3x + 6 + 2x - 6 = 120
5x = 120
x = 120/5
x = 24 yrs is H's age now
:
check it out in the statement
1%2F2(24+2) + 1%2F3(24-3) = 20
1%2F2(26) + 1%2F3(21) = 20
13 + 7 = 20 confirms our answer