Question

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?

Answer 1

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.

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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