2/5 of the students...

Question

2/5 of the students in a class are boys. 1/3 of the girls and 2/7 of the boys can swim. If three more girls than boys can swim how many students are there in the class?

Answer 1

Let x = the number of students in the class

 

First, set variables to represent how many boys and girls in the class.

 

Number of boys in the class = (2 / 5)x

Number of girls in the class = (3 / 5)x

 

This is because if we add the number of boys and girls together, we get the total number of students in that class.  

 

 

Now, we set variables to represent how many girls and boys can swim.

 

Number of girls who can swim = (1 / 3)(3 / 5)x = (1 / 5)x

Number of boys who can swim = (2 / 7)(2 / 5)x = (4 / 35)x

 

 

3 more girls than boys can swim.  This means the difference between their numbers is 3.

 

(1 / 5)x - (4 / 35)x = 3

 

 

We are subtracting fractions.  We need to find the LCD of the equation.  LCD is 35.

 

(7x - 4x) / 35 = 105 / 35

 

 

Equate numerators.

 

3x = 105

 

 

Divide both sides of the equation by 3.

 

x = 35

 

 

There are 35 students in the class.