Answer:
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.
