After Euclid High School's last basketball game, it was determined that $\frac{1}{4}$ of the team's points were scored by Alex and $\frac{2}{7}$ were scored by Brittany. Chelsea scored 15 points. None of the other 7 team members scored more than 2 points. What was the total number of points scored by the other 7 team members?

A. 10

B. 11

C. 12

D. 13

E. 14

1. 2019 AMC 8 官方解析

当欧几里得高中中的最后一场篮球赛结束，有$\frac{1}{4}$的得分确认是 Alexa 贡献，而$\frac{2}{7}$是由 Brittany 贡献的，Chelsea 得到15分．剩下的队里7个人没有超过2分的．问剩下七个人的总得分是多少？

Denote the total number students as $T$.

$0 \leqslant T - \frac{1}{4}T - \frac{2}{7}T - 15 \leqslant 14$

$15 \leqslant \frac{13}{28}T \leqslant 29$

Note that T is an integer, so this 13T must be divisible by 13. Only multiple of 13 is 26. The score by the the other 7 team members is 26-15 = 11.