Question

In one senior class, 1/3 of the students are honor students. Of these honor students, 2/7 are varsity athletes. If they are four athletes in the class, how many students are there in the class? a. 84 b. 42 c. 52 d. 60

Answer 1

B. 42

Explanation:

With the given information, we know that 2/7 of 1/3 of the class is equal to 4. This can be written as:

`2/7x * 1/3 = 4`, where `x` is the number of total students. All we need to do now is find `x`.

`2/7x = 12`

`2x = 84`

`x = 42`

Answer 2

There are (b) 42 students in the class.

Explanation:

From the given information, we know that `1/3` of the total number of students is the number of honour students:

`1/3 xx "(total students)" = "(honour students)"`

We also know that `2/7` of the honour students are athletes:

`2/7 xx "(honour students)" = "(athletes)"`

But we also know that the number of athletes in the class is `4`.
And since we also know that the number of honour students is "`1/3` the total number of students in the class", we substitute these values in like this:

`2/7 xx "(honour students)" = "(athletes)"`

`2/7 xx (1/3 xx "total students") = 4`

Let's allow `x` to represent the total number of students. Then our equation to solve is:

`2/7 xx 1/3 xx x = 4`

We can combine the two fractions on the left into one through multiplication:

`2/21 xx x = 4`

We can also isolate `x` by dividing both sides by `2/21` (which is the same a multiplying both sides by `21/2`):

`21/2(2/21 xx x) = 21/2xx4`

`x = 21/2 xx 4`

The 4 and the 2 reduce to "2 over 1":

`x = 21/1 xx 2`

And now we multiply `21 xx 2`:

`x = 42`