Chloe charged for admission to her play on three different nights. Each night, a different number of people were in attendance, but remarkably, Chloe collected $541 each night. If the admission charges for each child and each adult were $9 and $17, respectively, how many people in total came to the three showings?
I used guess and check to solve these types, and it took forever.
I was lucky to have the answer in time because it was a competition.
Is there any way better to solve this?
This is how I would solve it:
17 - 9 = 8 -number of adults the first night
8 x $17 =$136 and 45 children x $9 =$405 for a total of $541.
Then the adults number goes up by 9 and childrens' number comes down by 17.
8+9 =17 x $17 =$289 and 28 children x $9 =$252 for a total of $541.
17+6 =26 x 17 =$442 and 11 children x $9 =$99 for a total of $541.