Give and Take
On the first hole of a golf match, Jason lost to Mark as many dollars as Mark had with him at the golf course after paying his green fee. On the second hole, Mark lost to Jason the amount of money that Jason still had after paying his loss on the first hole. Then on the third hole, Jason lost to Mark the same number of dollars as Mark had left after Mark had paid his first loss. They then tied the next fifteen holes. This left Jason with no money and Mark with $80. With how much money did each golfer start the round?
Please submit all solutions to mathpotw@acu.edu by 5:00 PM on Thursday, October 22.
Solution to Give and Take
Correct solutions were submitted by: Ricky Kagoro Lumala, Jett Patterson, Hannah Smith, and Wyatt Witemeyer
We will merely keep up with the amount of money each player has, with Jason starting with X dollars and Mark starting with Y dollars.
| Jason | Mark | |
| Start | X | Y |
| 1 | X – Y | Y + Y |
| 2 | 2(X – Y) | 2Y – (X – Y) |
| 3 | 2(X – Y) – (3Y – X) | 2(3Y – X) |
Thus we need to solve the two equations 3X – 5Y = 0 and 2(3Y – X) = 80. The solution is
X = 50 and Y = 30.
