AMC8 2013 Problem 16

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?

Answer Choices
A. 16
B. 40
C. 55
D. 79
E. 89