Question 1122091: Julian and Patrick had some marbles. If Julian gave Patrick 20 marbles, both of them would have an equal number of marbles. If Patrick gave Julian 20 marbles, Julian would have three times as many marbles as Patrick. Find the number of marbles that each of them had.
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
From the condition, you have these two equations
(1) J - 20 = P + 20 ("If Julian gave Patrick 20 marbles, both of them would have an equal number of marbles")
(2) 3*(P - 20) = J + 20 ("If Patrick gave Julian 20 marbles, Julian would have three times as many marbles as Patrick")
From eq(1), express J = P+40 and substitute it into eq(2). You will get
3*(P-20) = (P+40) + 20, or
3P - 60 = P + 60,
3P - P = 60 + 60
2P = 120 ====> P = 120/2 = 60.
Answer. Patrick had initially 60 marbles; Julian had P+40 = 60+40 = 100 marbles.
Check on your own that the equations (1) and (2) are hold in this case.
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