Question 1057158
Let x represent the number of $12 tickets purchased.


Then, the number of $15 tickets is "three fewer ... than four-fifths the number" of $12 tickets.


The number of $15 tickets can then be represented as:


(4/5)x - 3


The amount collected from the sale of $12 tickets is 12 * x = 12x.


The amount collected from the sale of $15 tickets is 15 * [(4/5)x - 3] = 12x - 45.


Together, these amounts must add up to the total ticket sales of $675, which 
gives the following equation:


12x + (12x - 45) = 675


Collecting like terms on the left side gives:


24x - 45 = 675


Adding 45 to both sides then gives:


24x = 720


Dividing both sides by 24 then leaves:


x = 30


This is the number of $12 tickets. You can then substitute x = 30 into "(4/5)x - 3"
to get the number of $15 tickets.