Final answer:
To solve this problem, we need to set up a system of equations based on the given information. We can then solve the system to find the number of adult tickets and senior/child tickets sold. In this case, 111 adult tickets and 197 senior/child tickets were sold.
Step-by-step explanation:
To solve this problem, let's assign variables to the unknown quantities. Let's say the number of adult tickets sold is x and the number of senior/child tickets sold is y.
We know that the total value of tickets sold was $2,587.50. This can be expressed as an equation: 10x + 7.50y = 2,587.50.
We are also given that the number of senior/child tickets sold was 25 less than twice the number of adult tickets sold. This can be expressed as another equation: y = 2x - 25.
Now we have a system of two equations with two variables:
10x + 7.50y = 2,587.50 and y = 2x - 25.
We can solve this system of equations using substitution or elimination. Let's use substitution:
Substitute the value of y from the second equation into the first equation: 10x + 7.50(2x - 25) = 2,587.50.
Simplify and solve for x: 10x + 15x - 187.50 = 2,587.50. Combine like terms: 25x - 187.50 = 2,587.50. Add 187.50 to both sides: 25x = 2,775. Divide both sides by 25: x = 111.
Now substitute the value of x back into the second equation to solve for y: y = 2(111) - 25. Simplify: y = 197.
Therefore, 111 adult tickets and 197 senior/child tickets were sold at the movie theater.