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# Money Problem

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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?

May 1, 2019

#1
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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.

May 2, 2019
#2
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This is a short computer code to find the above numbers:

n=1; a=((541 - n*17) / 9);printn,a; n++; if(n<=50, goto1, discard=0;