Question 109609
Let x=total # of tickets needed to be sold


So if Six-sevenths of the total was sold, then we have the expression {{{(6/7)x}}}


Since we are told that 82 tickets are left over, then we simply subtract the expression {{{(6/7)x}}} (which is the number sold so far) from the total x to get 82:


{{{x-(6/7)x=82}}}



{{{(7)(x-(6/7)x)=(7)(82)}}} Multiply both sides by the LCM of 7. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a href=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)




{{{7x-6x=574}}} Distribute and multiply the LCM to each side




{{{x=574}}} Combine like terms on the left side





So that means that there are 574 tickets total



Now take six-sevenths of this total to get


{{{(6/7)574=492}}}



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Answer:


So 492 tickets have been sold so far.


Notice how 492 and 82 add up to 574. So this verifies our answer.