# 2013 AMC8 Problem 16

#### theory

##### algebra geometry
A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $$8^\text{th}$$-graders to $$6^\text{th}$$-graders is $$5:3$$, and the ratio of $$8^\text{th}$$-graders to $$7^\text{th}$$-graders is $$8:5$$. What is the smallest number of students that could be participating in the project?

$$\textbf{(A)}\ 16 \qquad \textbf{(B)}\ 40 \qquad \textbf{(C)}\ 55 \qquad \textbf{(D)}\ 79 \qquad \textbf{(E)}\ 89$$