Question

A matinee ticket costs $6 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who saw a movie was 35, and the total money collected was $70. Which of the following options represents the number of children and the number of adults who saw a movie that day, and the pair of equations that can be solved to find the numbers?

7 children and 28 adults
Equation 1: a + c = 35
Equation 2: 6a − c = 70
7 children and 28 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a − c = 70

Answer 1

28 children and 7 adults

Equation 1: a + c = 35

Equation 2: 6a + c = 70

Explanation:

If the total number of people at the movie was 35 people, one of the equations will be a + c = 35.

If $70 was collected in total, the other equation will be 6a + c = 70.

Now, solve this system of equations:

a + c = 35

6a + c = 70

Solve by elimination by multiplying the top equation by -1, then adding the equations together:

-a - c = -35

6a + c = 70

Add these together, and solve for a:

5a = 35

a = 7

Since there were 35 people in total, find how many children attended by subtracting 7 from 35:

35 - 7

= 28

So, there were 28 children and 7 adults.

The equations used were: a + c = 35 and 6a + c = 70

So, the correct answer is:

28 children and 7 adults

Equation 1: a + c = 35

Equation 2: 6a + c = 70