SOLUTION: The sum of Patrick's age and John's age is 58.Eight years ago , Patrick was twice as old as John then. What is John's age ?

Question 658829: The sum of Patrick's age and John's age is 58.Eight years ago , Patrick was twice as old as John then. What is John's age ?
Answer by Shana-D77(132) (Show Source): You can put this solution on YOUR website!
If Patrick's age now is x and John's age now is y, then x + y = 58.
Eight years ago, Patrick's age was x - 8. John's age was y - 8. This is the trickiest part of the problem.
So, we have to build the second equation:
"Eight years ago , Patrick was twice as old as John then.":
x - 8 = 2(y - 8)
x - 8 = 2y - 16 (distributed)
x - 2y = -8 (subtracted 2y from both sides and added 8 to both sides)

out two equations are:
x + y = 58
x - 2y = -8
----------------
3y = 66 (used elimination by subtraction to "get rid of" the x)
y = 22
So, John is 22 years old now and Patrick's age now is (58 - 22) or 36.
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