2013 AMC8 Problem 16

theory

algebra geometry
#1
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?

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