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
S541 each night. If the admission charges for each child and each adult were $9
and S17, respectively, how many people in total came to the three showings?

The number of people in total that came to the three showings is 138 people

Step-by-step explanation:

The amount Chloe collected each night for admission to her play = $541

The admission  charge for each child = $9

The admission  charge for each adult = $17

The number of people attending the play each of the three nights are different

Let x represent the number of children that attend the play on the first night and ley y represent the number of adults that attend, we have;

9·x + 17·y = 541

For the second night, we have;

9·a + 17·b = 541

For the third night, we have;

9·c + 17·d = 541

27·(x + a + c) + 51·(y + b + d) = 1,623

Using Microsoft Excel, where we create a series with the first term = 541 and the common difference, d = -9 and number the adjacent column serially from 1 to 61 and the on the right column we divide the created series by 17 then we search for the whole number combinations, we get three possible combinations as follows;

12 children and 26 adults

29 children and 17 adults

46 children and 8 adults

Therefore, the number of people in total that came to the three showings = 12 + 26 + 29 + 17 + 46 + 8 = 138

The number of people in total that came to the three showings = 138 people.