SOLUTION: 4 years ago Judy was twice as old as Sam. 4 years from now Sam will be 3/4 of Judy's age. How old is Judy now?
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Question 411021: 4 years ago Judy was twice as old as Sam. 4 years from now Sam will be 3/4 of Judy's age. How old is Judy now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let s = Sam's present age
Let j = Judy's
:
Write an equation for each statement:
:
"4 years ago Judy was twice as old as Sam."
j - 4 = 2(s - 4)
j - 4 = 2s - 8
j = 2s - 8 + 4
j = 2s - 4
:
" 4 years from now Sam will be 3/4 of Judy's age."
s + 4 = (j + 4)
multiply both sides by 4, results:
4(s+4) = 3(j + 4)
4s + 16 = 3j + 12
4s = 3j + 12 - 16
4s = 3j - 4
Replace j with (2s-4) from the 1st statement
4s = 3(2s - 4) - 4
4s = 6s - 12 - 4
4s = 6s - 16
16 = 6s - 4s
16 = 2s
s =
s = 8 yrs is sam's present age
:
Find j
j = 2s - 4
j = 2(8) - 4
j = 12 yrs is Judy's present age
:
:
Check solution in the 1st statement
"4 years ago Judy was twice as old as Sam. "
12 - 4 = 2(8 - 4)
8 = 2(4); confirms our solution
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