Question

The admission at the movies is $7.25 for children and $9.75 for adults. The total amount collected was $3000.00. There were a total of 350 people. Create and solve a system of linear equations to figure out how many of the people were children and how many were adults. Choose the appropriate method for solving and provide a viable argument for your choice.

A. Graphing
B. Substitution
C. Elimination
D. None of the above

Answer 1

Using a system of linear equations and the elimination method, it was determined that there were 165 children and 185 adults at the movies, which amounts to a total of 350 people and $3000 in ticket sales. Therefore, the correct choice is: C. Elimination.

Step-by-step explanation:

Let's denote the number of children as C and the number of adults as A.

The problem gives us two pieces of information:

1. The total admission collected was $3000. This gives us the equation:

7.25C + 9.75A = 3000.

2. There were a total of 350 people:

C + A = 350.

Now, you can choose any suitable method to solve this system of linear equations. In this case, the most efficient method would be the elimination method (option C). By multiplying the second equation by 7.25 to make the coefficients of C in both equations the same, you can eliminate C when adding the two equations, simplifying the process. Therefore, the correct choice is: C. Elimination.