SOLUTION: S is 1/4 if the age of father. in 12 years he will be 2/5 of the age of father so what is their ages now? please show me the equations to solve.

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Question 87499: S is 1/4 if the age of father. in 12 years he will be 2/5 of the age of father so what is their ages now?
please show me the equations to solve.
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
S is 1/4 if the age of father. in 12 years he will be 2/5 of the age of father so what is their ages now?
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Ages NOW DATA:
Let S be x yrs. old ; Father is 4x yrs old.
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In 12 years DATA:
S will be x+12 ; Father will be 4x+12
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EQUATION:
x+12 = (2/5)(4x+12)
5x+60 = 8x+24
3x = 36
x = 12 yrs old (S's age NOW)
4x = 48 yrs old (Father's age NOW)
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Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let S = age of S and F = age of father.
1) S+=+%281%2F4%29F "S is 1/4 of the age of father".
2) S%2B12+=+%282%2F5%29%28F%2B12%29 "In 12 years (S+12) he will be 2/5 of the age of father (F+12)".
Substitute the S from eqation 1) into equation 2) and solve for F.
%281%2F4%29F%2B12+=+%282%2F5%29%28F%2B12%29 Simplify.
%28F%2F4%29%2B12+=+%282F%2F5%29%2B24%2F5 Multiply through by the LCD of 20 to clear the fractions.
5F%2B240+=+8F%2B96 Subtract 5F from both sides.
240+=+3F%2B96 Subtract 96 from both sides.
144+=+3F Finally, divide both sides by 3.
48+=+F
So, Father's present age is 48 years.
S+=+%281%2F4%29F
S+=+%281%2F4%2948
S+=+12
So, S's present age is 12 years.