SOLUTION: Four friends are playing poker. At the end of the night the total pot won equals $223. Melvin has $20 more than Bob, $50 more than John, and $71 more than Ray. How much does eac

Question 99592: Four friends are playing poker. At the end of the night the total pot won equals $223. Melvin has $20 more than Bob, $50 more than John, and $71 more than Ray. How much does each have? We are trying to solve this problem at work and nobody can figure it out!
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Use the first initials of each player as unknowns. The amount of money won by Mel is represented
by M, by Bob is represented by B, by John is represented by J, and by Ray is represented
by R.
.
The total amount of money won is the sum of the winnings of the four players. So you can
write the equation:
.
M + B + J + R = 223
.
Next you are told that Mel won $20 more than Bob. Therefore, if you took $20 from Mel's winnings
the amount you would get is what Bob won. Therefore, M - 20 = B. So in the equation you
can substitute M - 20 for B and the equation becomes:
.
M + M - 20 + J + R = 223
.
Similarly, if you took $50 away from Mel's winnings you would have John's winnings.
In equation form this would be M - 50 = J. Substitute M - 50 for J in the equation and
it becomes:
.
M + M - 20 + M - 50 + R = 223
.
Finally, if you took away $71 from Mel's winnings, you would have Ray's amount of winnings.
In equation form this is M - 71 = R. Substitute M - 71 for R and the equation then is:
.
M + M - 20 + M - 50 + M - 71 = 223
.
Collect all the M's on the left side of this equation. There are four of them so the equation
becomes:
.
4M - 20 - 50 - 71 = 223
.
Next collect the numbers on the left side. -20 and -50 and -71 combine to -141. This makes
the equation:
.
4M - 141 = 223
.
Get rid of the -141 on the left side by adding 141 to both sides of the equation:
.
4M = 364
.
Solve for M by dividing both sides of the equation by 4 to get:
.
M = 364/4 = $91
.
Mel won $91
.
That means that Bob, who won $20 less than Mel, won $71
.
and John, who won $50 less than Mel, won $41.
.
and finally, Ray, who won $71 less than Mel, won $20.
.
Check by adding everybody's winnings. $91 + $71 + $41 + $20 = $223. It checks. So the
answers are likely to be correct.
.
Take the rest of the day off. Hope this helps you to have a good weekend. I've got to go
find a game like this one ... everybody wins something and nobody loses! Terrific!
.
/// I love slashies
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