Question 1187556
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Anton, Chris and Eddie had some tickets to sell for their school concert. 
After Anton sold 1/3 of his tickets, Chris sold 2/5 of his and Eddie sold 3/4 of his, 
they had an equal number of tickets left. 
If they sold tickets 225 altogether, how many tickets did each boy have left?
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<pre>
Let 3x be the number of tickets Anton had initially;  then he sold   x  tickets and has  2x  tickets left.

    
Let 5y be the number of tickets Chris had initially;  then he sold  2y  tickets and has  3y  tickets left.


Let 4z be the number of tickets Eddie had initially;  then he sold  3z  tickets and has   z  tickets left.


From the condition, we have these equations


    2x = z               (1)

    3y = z               (2)

    x + 2y + 3z = 225    (3)


From (1), exoress x = z/2  and substitute into equation (3);  from (2), express y = z/3 and substitute into equation (3).

Then equation (3) takes the form


    {{{z/2}}} + {{{2*(z/3)}}} + 3z = 225.


Multiply both sides by 6 (all the terms); then simplify and find z


    3z + 4z + 18z = 6*225

         25z      = 6*225

           z      = {{{(6*225)/25}}} = 6*9 = 54.


So, according to the condition, each boy has 54 tickets left.    <U>ANSWER</U>
</pre>

Solved.


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