SOLUTION: Bill has twice as much money as Jim. If I give Jim $2.50, he will have three times as much money as Bill. How much money did Bill and Jim have originally?

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Question 803738: Bill has twice as much money as Jim. If I give Jim $2.50, he will have three times as much money as Bill. How much money did Bill and Jim have originally?
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
For solving this problem, Bill will be y and Jim will be x.
To start off, we know that Bill has double the amount that Jim has.
You can think of this as 2 Jims equal 1 Bill.
You would write this as y=2x.
Now if Jim were to be given $2.50 he would have 3 times as much as Bill.
This equation can be written as 2.50%2Bx=3y.
Jim plus the $2.50 is equal to 3 times Bill.
We are going to solve for Jim first.
We want to solve for x since Jim is x.
That means u will plug y=2x into 2.50%2Bx=3y.
Since y=2x, you can replace the y in 2.50%2Bx=3y with 2x.
Solve for x.
2.50%2Bx=3%282x%29 Multiply 3*2x
2.50%2Bx=6x+ Subtract x from both sides
2.50=5x+ Divide both sides by 5
x=.50
We know now Jim originally had $.50.
Now let's figure out what Bill originally had.
We need to solve for y.
2.50%2Bx=3y can also be written x=3y-2.50.
Now plug x=3y-2.50 into y=2x.
You can replace the x in y=2x with 3y-2.50.
Now solve.
y=2%283y-2.50%29 Multiply it out.
y=%282%2A3y%29-%282%2A2.50%29
y=6y-5 Subract 6y from both sides.
-5y=-5+ Divide each side by -5.
y=1
We have now figured out that Bill started with $1.00.
The answer for this problem is Jim originally had $.50 and Bill originally has $1.00.