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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;

 

Adults            Children

8                      45

17                    28

26                    11

 May 2, 2019

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