GWD 24 3马上要考了，大家帮助一下

in a certain game played with red chips and blue chips, each red chip has a point value of X and each blue chip has a point value of Y, where X>Y and X and Y are positive integers. If a player has 5 red chips and 3 blue chips, what is the average (arithmetic mean ) point value of the 8 chips that the player has?

(1)   The average point value of one red chip and one blue chip is 5.

(2)   The average point value of the 8 chips that the player has is an integer.

这题答案是C，不过我认为是E，希望大家多帮忙讨论，感谢!

red有X个,blue有Y个,列方程:

5X+3Y=8

X+Y=10,变形X=10-Y.代入上个方程,得25-Y)/4是integer.

而Y是从1到9的取值,一个个往里代,同时根据X=10-Y求X,这样符合条件的只有Y=1

一个red有X个points,一个blue有Y个points.因为单独条件1和单独条件2都无法算出the average (arithmetic mean ) point value of the 8 chips that the player has

由条件1列方程: X+Y=2*5=10

又因为X>Y，所以只有以下几种可能：X=6 Y=4，X=7 Y=3，X=8 Y=2，X=9 Y=1

由条件2列方程： 5X+3Y=8a，其中a为正整数

因此只有X=9,Y=1符合上式，所以答案是c