Mega Movies hosted a film premiere on Friday night. They charged $7 for adults and $5 for children. One hundred twenty-three adults and children attended, and $829 was made in ticket sales. How many children and how many adults went to the film premiere?
A = # adults
C = # children
7A + 5C = $829
A + C = 123 attendees
Solve the two equations simultaneously. Post your work if you get stuck.
To solve this problem, let's assume the number of adults who attended the premiere is "A", and the number of children who attended is "C".
Now we have two pieces of information given in the problem:
1. The total number of adults and children who attended the premiere is 123: A + C = 123
2. The total ticket sales were $829, with adults paying $7 per ticket and children paying $5 per ticket: 7A + 5C = 829
We can solve this system of equations to find the values of A and C.
Step 1: Solve equation 1 for one variable:
A = 123 - C
Step 2: Substitute this value of A into equation 2:
7(123 - C) + 5C = 829
861 - 7C + 5C = 829
2C = 829 - 861
2C = -32
C = -32 / 2
C = -16
Step 3: Substitute the value of C back into equation 1 to find A:
A + (-16) = 123
A = 123 + 16
A = 139
Therefore, there were 139 adults and 16 children who attended the film premiere.