SOLUTION: Please help me solve this word problem: John's present age is three-fourths of Sally's present age. In five years, John's age will be four-fifths of Sarah's age at that time. Wh

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Question 234276: Please help me solve this word problem:
John's present age is three-fourths of Sally's present age. In five years, John's age will be four-fifths of Sarah's age at that time. What are the present ages of John and Sally?
----- Thank you =)
Found 2 solutions by Earlsdon, checkley77:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let J = John's present age and S = Sally's present age.
1) J+=+%283%2F4%29S "John's present age is three-fourths of Sally's present age."
2) J%2B5+=%284%2F5%29%28S%2B5%29 "In five years, John's age will be four-fifths of Sally's (not Sarah's) age at that time."
Substitute J+=+%283%2F4%29S into equation 2) and solve for S.
2a) %283%2F4%29S%2B5+=+%284%2F5%29%28S%2B5%29 Multiply through by the LCD of 20 to clear the fractions.
2b) 15S%2B100+=+16%28S%2B5%29
2c) 15S%2B100+=+16S%2B80
2d) 20+=+S and...
1a) J+=+%283%2F4%29%2820%29
1b) J+=+15
Sally's present age is 20 and John's present age is 15.

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
John's age now=3x/4
Sally's age now=x
In 5 years John will be 3x/4+5
Sally will be 4/5(x+5)
3x/4+5=4/5(x+5)
3x/4+5=(4x+20)/5
(3x+4*5)/4=(4x+20)/5 crosss multiply.
5(3x+20)=4(4x+20)
15x+100=16x+80
15x-16x=80-100
-x=-20
x=20 ans. for sally's age now.
3/4*20=60/4=15 ans. for John's age now.
Proof:
3/4*20+5=4/5(20+5)
15+5=4/5*25
20=100/5
20=20