Answer:
Bill starts with $5 and Joe starts with $25
Step-by-step explanation:
Let Ji and Bi represent the initial amounts that Joe and Bill have at the start. Number after J and B will be used to indicate subsequent steps in the problem.
We are told that "Joe has five times as much money as Bill," which we can write as:
1) Ji = 5Bi
We learn that "Joe pays Bill $5," which we can represent as:
2) J1 = Ji - 5
This would mean that Bill has added $5:
3) B1 = Bi + 5
We are then told that "Joe has just twice the amount Bill now has," which we can write as:
4) J1 = 2B1
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We can rearrnage and substitute the above relationships to eliminate one of the two variables (B1 or J1)
J1 = Ji - 5 [from 2]
2B1 = Ji - 5 [Substitute 4 to eliminate J1]
Ji = 5Bi [from 1]
2B1 = 5Bi - 5 [Substitute 1 to eliminate Ji]
B1 = Bi + 5 [Rearrange]
2(Bi + 5) = 5Bi - 5 [Use the above expression in the previous equation to eliminate B1]
2Bi + 10 = 5Bi - 5 [Simplify]
-3Bi = -15 [Simplify]
Bi = $5 [Solve]
Ji = 5Bi [from 1]
Ji = 5*(5) [Since Bi = $5]
Ji = $25 [Solve]
Bi = $5 and Ji = $25
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CHECK:
Does Joe has five times as much money as Bill?
Ji = $25 and Bi = $5 YES
When Joe pays Bill $5 he owes him, does Joe has just twice the amount Bill now has?
J1 = $25 - $5 = $20
B1 = $5 + $5 = $10 YES
