Question

Mrs. Molitor runs the ski club. if the ratio of instructors to students in the ski club is 3 to 7, how many instructors are there if there are 12 more students than instructors? also, how many students are there?

Answer 1

9 instructors and 21 students

Step-by-step explanation

The ratio of instructors to students in the ski club is 3 to 7, that is:

3 : 7

We want to know how many instructors there are if there are 12 more students than instructors.

We also want to know how many students are there.

To do this, let the number of instructors be x.

Let the number of students be y.

Therefore, we have that:

y = 12 + x

The ratio of instructors to students now is:

x : y

=> x : 12 + x

We can compare with the initial ratio given:

`(3)/(7)\text{ = }\frac{x}{12\text{ + x}}`

We can cross multiply:

`\begin{gathered} 3(12\text{ + x) = 7x} \\ 36\text{ + 3x = 7x} \\ \Rightarrow\text{ 7x - 3x = 36} \\ 4x\text{ = 36} \\ x\text{ = }(36)/(4)=\text{ 9} \end{gathered}`

Therefore, there are 9 instructors.

The number of students there is:

y = 12 + 9 = 21

There are 21 students.