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

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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(52797) About Me  (Show Source):
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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?
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Let x be the total number of the students in the class.


x%2F5%2B3 students like badminton.

The number of remaining  students is  x-%28x%2F5%2B3%29 = %284x%29%2F5-3.

Hence, the number of students that like swimming is  %281%2F3%29%2A%28%284x%29%2F5-3%29+7 = %284x%29%2F15-1%2B7 = %284x%29%2F15%2B6.


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

     x = x%2F5%2B3 + %284x%29%2F15%2B6 + 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  x%2F5%2B3 = 60%2F5%2B3 = 12+3 = 15.


The number of those who like swimming is  %284x%29%2F15%2B6 = %284%2A60%29%2F15%2B6 = 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.