# 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

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:

There are **(b)** 42 students in the class.

#### Explanation:

From the given information, we know that

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

We also know that

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

But we also know that the number of athletes in the class is

And since we also know that the number of honour students is "

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

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

Let's allow

#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

#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

#x = 42#