SOLUTION: Two years ago Sam's age was 2/3 of Pam's. Three years from now Sam's age will be 3/4 of Pam's age. In 20 yrs, their combined ages will be 69. How old is Sam now?

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Question 390439: Two years ago Sam's age was 2/3 of Pam's. Three years from now Sam's age will be 3/4 of Pam's age. In 20 yrs, their combined ages will be 69. How old is Sam now?
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Two years ago Sam's age was 2/3 of Pam's. Three years from now Sam's age will be 3/4 of Pam's age. In 20 yrs, their combined ages will be 69. How old is Sam now?
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Equations:
(s-2) = (2/3)(p-2)
(s+3) = (3/4)(p+3)
(s+20)+(p+20) = 69
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Modify each equation:
3s-6 = 2p-4
4s+12 = 3p+9
s+p = 29
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Modify Again:
3s-2p = 2
4s-3p = -3
s+p = 29
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Subtract 1st from 2nd and leave the 3rd alone
s-p = -5
s+p = 29
----
2s = 24
s = 12 (Sam's age now)
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Cheers,
Stan H.
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Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Two years ago Sam's age was 2/3 of Pam's. Three years from now Sam's age will be 3/4 of Pam's age. In 20 yrs, their combined ages will be 69. How old is Sam now?
2 years ago
let Pam's age be x,
Sam age = 2x/3
..
After 20 years
pams age = x+22
Sam's age = 2x/3 +22
..
x+22+2x/3 +22=69
x+2x/3 +44=69
(3x+2x)/3 = 69-44
5x/3 = 25
5x= 25*3
5x=75
/5
x=15 Pam's age 2 years ago.
Sam's age 2 years ago =2x/3 = 2*15/3=10 years.
..
Sam's age now = 10+2 = 12 years
..
m.ananth@hotmail.ca