Question 1090755: Tim and Jeff have some money. If Jeff gives $5 to Tim, then they will have the same amount of money.
If Tim gives $5 to Jeff, then Jeff would have twice as much as Tom. how much money does each have at first?
Found 2 solutions by ikleyn, jorel1380:
Answer by ikleyn(52756)   (Show Source):
You can put this solution on YOUR website! .
Tim and Jeff have some money. If Jeff gives $5 to Tim, then they will have the same amount of money.
If Tim gives $5 to Jeff, then Jeff would have twice as much as Tom. how much money does each have at first?
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Let Tim has T dollars, and let Jeff has J dollars.
If Jeff gives $5 to Tim, Jeff will have (J-5) dollars, while Tim will have (T+5) dollars.
According to the condition, these amounts are identical, which gives you an equation
J - 5 = T + 5. (1)
If in opposite, Tim gives $5 to Jeff, Tim will have (T-5) dollars, while Jeff will have (J+5) dollars.
According to the condition, in this case you obtain this equation
J + 5 = 2*(T-5). (2)
The equations (1) and (2) form the system of two equations for two unknowns.
From (2), express J = T + 5 + 5 = T + 10 and substitute it into (2), replacing J:
(T+10) + 5 = 2*(T-5),
T + 15 = 2T - 10,
10 + 15 = T ====> T = 25.
Answer. Tim has $25. Jeff has T+10 = 25 + 10 = 35 dollars.
Answer by jorel1380(3719)  (Show Source):
You can put this solution on YOUR website! Let t and j be Tim's money and Jeff's money, respectively. Then:
j-5=t+5
j+5=2(t-5)
So:
j=t+10
t+10+5=2t-10
t=25
j=35
Tim has $25; Jeff has $35
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