Question

Antonio loves to go to the movies. He goes both at night and during the day. The cost of a matinee is $6. The cost of an evening show is $8. Antonio went to see a total of 5 movies and spent $36. How many of each type of movie did he attend? Write a system of equations..

Answer 1

To find the number of each type of movie Antonio attended, we can set up a system of equations based on the given information. By solving this system using the substitution method, we find that Antonio attended 2 matinee movies and 3 evening movies.

Step-by-step explanation:

To solve this problem, let's define two variables: x and y.

x represents the number of matinee movies Antonio attended and y represents the number of evening movies Antonio attended.

We can now write two equations based on the given information:

1. The total number of movies Antonio attended is 5: x + y = 5
2. The total cost of the movies Antonio attended is $36: 6x + 8y = 36

Now we have a system of equations with two variables. We can solve this system using various methods, such as substitution or elimination.

Let's use the substitution method:

1. From the first equation, we can rewrite it as x = 5 - y.
2. Substitute x in the second equation with the value 5 - y: 6(5 - y) + 8y = 36.
3. Simplify the equation: 30 - 6y + 8y = 36.
4. Combine like terms: 2y = 6.
5. Divide both sides by 2: y = 3.
6. Substitute y with the value 3 in the first equation: x + 3 = 5.
7. Simplify the equation: x = 2.

Therefore, Antonio attended 2 matinee movies and 3 evening movies.

Answer 2

2 matinee ($12)

3 evening ($24)

Step-by-step explanation:

x + y = 5

6x + 8y = 36

x = 2 and y = 3 (the only answers that satisfy both equations)