SOLUTION: two years ago, sue was half as old as pat. eight years from now, sue will be two-thirds as old as pat. how old is each of them now?

Question 340381: two years ago, sue was half as old as pat. eight years from now, sue will be two-thirds as old as pat. how old is each of them now?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two years ago, sue was half as old as pat. eight years from now, sue will be two-thirds as old as pat. how old is each of them now?
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Equations:
(s-2) = (1/2)(p-2)
(s+8) = (2/3)(p+8)
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Rearrange:
2s-4 = p-2
3s+24= 2p+16
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Rearrange:
2s-p = 2
3s-2p = -8
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Multiply thru 1st eq. by 2 to get:
4s-2p = 4
3s-2p = -8
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Subtract 2nd from 1st to get:
s = 12 (Sue's age now)
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Since 4s-2p = 4, substitute for "s" and solve for "p":
4*12-2p = 4
48-2p = 4
2p = 44
p = 22 (Pat's age now)
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Cheers,
Stan H.
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