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

2 Answers
May 16, 2018

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

May 16, 2018

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