Question 118930
Let's say that they bought x $27 tickets.  That means that they bought (29 - x) $21 tickets.


The value of the $27 tickets then is {{{27x}}} and the value of the $21 tickets is {{{21(29-x)}}}.


Finally, we know that the value of the $27 tickets plus the value of the $21 tickets is $675, so we can write:


{{{27x + 21(29-x) = 675}}}


Solve the equation:


{{{27x-21x+609=675}}}


{{{6x=66}}}


{{{x=11}}}


So now we know that they bought 11 $27 tickets, so they bought (29 - 11 = 18) $21 tickets.


Check:

11 * 27 = 297
18 * 21 = 378

11 + 18 = 29 and 
297 + 378 = 675 -- Answer Checks.