Emily went to the movie theater for her birthday. A mix of adults and children attended, making a total of 22 people. Each adult ticket was $9 and each child's ticket was $5.50. Is the total cost for the party was $125.5, then how many adults and how many children attended

13 children and 9 adults if the total cost is $152.5

Step-by-step explanation:

Let x children and y adults

x + y = 22 (1)

5.5x + 9y = 125.5 (2)

y = 22 - x

5.5x + 9 (22 - x) = 125.5

5.5x + 198 - 9x = 125.5

-3.5x = 125.5 - 198

-3.5x = - 72.5

x = 20.7

y = 22 - x = 1.3

Which is not possible

If the total cost is $152.5

x + y = 22 (1)

5.5x + 9y = 152.5 (2)

y = 22 - x

5.5x + 9 (22 - x) = 152.5

5.5x + 198 - 9x = 152.5

-3.5x = 152.5 - 198

-3.5x = - 45.5

x = 13

y = 22 - 13 = 9