jmc

Question

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

Accepted Answer

We multiply the first ratio by 8 on both sides, and the second ratio by 5 to get the same number for 8th graders, in order that we can put the two ratios together: 5:3 = 5(8):3(8) = 40:24 8:5 = 8(5):5(5) = 40:25 Therefore, the ratio of 8th graders to 7th graders to 6th graders is 40:25:24. Since the ratio is in lowest terms, the smallest number of students participating in the project is 40+25+24 = 89.