500 tickets were sold for a game for a total of $862.50. If adult tickets sold for $2.00 and children's tickets sold for $1.50, how many of each kind of tickets were sold?
Accepted Solution
A:
You can work these in your head if you consider the revenue generated by the least contributor (children's tickets) and the difference in revenue between that and the larger contributor ($2.00 -1.50 = 0.50).
If all were children's tickets, the revenue would be 500*$1.50 = $750.00. The actual revenue exceeded that amount by $862.50 -750.00 = 112.50. This difference in revenue is made up by the sale of $112.50/$0.50 = 225 adult tickets. Then the number of children's tickets is 500 -225 = 275.
225 adult tickets were sold 275 children's tickets were sold.
_____ If you need an equation, you can write an equation using a variable for the number of adult tickets sold (the largest contributor). .. (500 -a)*1.50 +a*2.00 = 862.50 .. 0.50a = (862.50 -750.00) . . . . . does this look familiar, yet? .. a = 112.50/0.50 = 225