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?
~~~~~~~~~~~~~~~~~~~~


<pre>
Let x be the total number of the students in the class.


{{{x/5+3}}} students like badminton.

The number of remaining  students is  {{{x-(x/5+3)}}} = {{{(4x)/5-3}}}.

Hence, the number of students that like swimming is  {{{(1/3)*((4x)/5-3)}}}+7 = {{{(4x)/15-1+7}}} = {{{(4x)/15+6}}}.


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

     x = {{{x/5+3}}} + {{{(4x)/15+6}}} + 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/5+3}}} = {{{60/5+3}}} = 12+3 = 15.


The number of those who like swimming is  {{{(4x)/15+6}}} = {{{(4*60)/15+6}}} = 4*4+6 = 16+6 = 22.


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


<U>ANSWER</U>.  7 students prefer swimming to badminton.
</pre>

Solved.