SOLUTION: 1/5 of the students in a class and an additional 3 students like badminton. 1/3 of the remaining students in the class and an additional 7 students like swimming and the remaining

Question 1206189: 1/5 of the students in a class and an additional 3 students like badminton. 1/3 of the remaining students in the class and an additional 7 students like swimming and the remaining 23 students in the class like cycling. How many more students prefer swimming to badminton?
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
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1/5 of the students in a class and an additional 3 students like badminton.
1/3 of the remaining students in the class and an additional 7 students like swimming
and the remaining 23 students in the class like cycling.
How many more students prefer swimming to badminton?
~~~~~~~~~~~~~~~~~~~~

Let x be the total number of the students in the class.


 students like badminton.

The number of remaining  students is   = .

Hence, the number of students that like swimming is  +7 =  = .


Then x = those who like badminton + those who like swimming + 23,  or

     x =  +  + 23.


The setup is complete. To solve equation, multiply both sides by 15

    15x = (3x+45) + (4x+90) + 345.


Simplify

    15x = 7x + 480

    15x - 7x = 480

        8x   = 480

         x = 480/8 = 60.


The number of those who like badminton is   =  = 12+3 = 15.


The number of those who like swimming is   =  = 4*4+6 = 16+6 = 22.


The difference (which is the problem's question) is 22 - 15 = 7.


ANSWER.  7 students prefer swimming to badminton.

Solved.

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