SOLUTION: Geoffrey is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, Geoffrey will be three times as old as Alice. How old is Peter now?

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Question 1105316: Geoffrey is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, Geoffrey will be three times as old as Alice. How old is Peter now?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Geoffrey is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, Geoffrey will be three times as old as Alice. How old is Peter now?
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Equations:
g = 2P
P = A+5
g+5 = 3(A+5)
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Substitute for "g" and "A" to get::
2P +5 = 3(P-5)+3*5
2P + 5 = 3P
P = 5 yrs (Peters age now)
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Cheers,
Stan H.
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Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.
Geoffrey is twice as old as his friend Peter. Peter is 5 years older than Alice.
In 5 years, Geoffrey will be three times as old as Alice. How old is Peter now?
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G = 2P              (1)
P = A + 5           (2)
G+5 = 3*(A+5)       (3)


===================> Substitute (1) into equation (3). In this way you eliminate unknown G 
                     and obtain the modified system for 2 unknowns A and P:


P = A + 5           (2')
2P + 5 = 3(A+5)     (3')


Now substitute (2') into (3'). You will get

2*(A+5) + 5 = 3(A+5)  ====>  2A + 15 = 3A + 15 ====>  A = 0.

Thus Alice is a newborn.

Then  from (2)  P = A + 5 = 0+5 = 5.


Answer. Peter is 5 years old.