SOLUTION: Problem: "Some parking meters in Milan, Italy, accept coins in the denominations of 20 cent, 50 cent, and 2 Euro. As as incentive program, the city administrators offer a big rew

Question 8459: Problem:
"Some parking meters in Milan, Italy, accept coins in the denominations of 20 cent, 50 cent, and 2 Euro. As as incentive program, the city administrators offer a big reward (a brand new red Ferrari) to any meter maid who brings back exactly 1000 coins worth exactly 1000 Euro from the daily rounds. What are the odds of this reward being claimed anytime soon?"
My work thus far:
X=20cent
Y=50cent
Z=2 Euro
X + Y + Z = 1000
.2X + .5Y + 2Z = 1000
.....
There is my problem, i'm not sure how to produce another equation so that I can start eliminating variables. I dont really need you to solve the problem, as much as helping me set it up.
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
Your equations and idea are correct.
However, tn fact,there is no third equation to help you to solve this system.
This kind of system,we can call it linear integer equations:
[It may have nfinite many integer solutions or no integer solutions]
X + Y + Z = 1000..(1)
.2X + .5Y + 2Z = 1000...(2)
(2)*10 to get rid of decimals:
2X + 5Y + 20 Z = 10000...(3)
(3)-(1)*2: 3y + 18 z = 8000
We see that the left hand side is divisible by 3, but the right
hand side is not. Hence, this system has no integer solutions.
In other words,there are no coins X,Y,Z can make the two 1000s.
And, hence, nobody can get the reward el mundo.
Kenny

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