Question

A number of students from SMS are participating in a community service project. The ratio of 8th graders to 6th graders is 5:3 and the ratio of 8th graders to 7th graders is 8:5. What is the smallest number of students that participated?

Answer 1

The smallest number of students that participated in community service project is 89

Solution:

Given that,

The ratio of 8th graders to 6th graders is 5:3 and the ratio of 8th graders to 7th graders is 8:5

We have to find what is the smallest number of students that participated?

Now, given ratios can be converted to fractions.

a : b can be converted to fraction as
`(a)/(b)`

`\text { 8th graders to } 6 \text { th graders is } 5: 3 \rightarrow \frac{\text { 8th graders }}{6 t h \text { graders }}=(5)/(3)`

On inversing we get,

`\rightarrow \frac{6 t h \text { graders }}{\text { 8th graders }}=(3)/(5)`

`8 \text { th graders to } 7 \text { th graders is } 8: 5 \rightarrow \frac{\text { 8th graders }}{7 \text { th graders }}=(8)/(5)`

On inversing we get,

`\rightarrow \frac{7 t h \text { graders }}{\text { 8th graders }}=(5)/(8)`

Now, add both the fractions

`\frac{6 \text {th graders}}{\text { 8th graders }}+\frac{7 \text {th graders}}{\text { 8th graders }}=(3)/(5)+(5)/(8)`

`\frac{6 t h \text { graders } + 7 \text { th graders }}{\text { 8th graders }}=(24+25)/(40)=(49)/(40)`

Now, we want least number of students, then we have to take from above fraction,

6th graders + 7th graders = 49

And 8th graders = 40,

Then, total students = 6th graders + 7th graders + 8th graders = 49 + 40 = 89

Hence, 89 students participated.