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