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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 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? 
Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
We multiply the first ratio by 8 on both sides, and the second ratio by 5 to get the same number for 8 th graders, in order that we can put the two ratios together: $$ \begin{aligned} \&5: 3=5(8): 3(8)=40: 24 \textbackslash\textbackslash{} \&8: 5=8(5): 5(5)=40: 25 \end{aligned} $$ 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 $$ 40+25+24=\text { (E) } 89 $$ 