Question

PLEASE HELP NEED NOW!!!

Solve this application problem using a system of equations: The Springfield Movie Theater sold adult tickets for $4.10 each and children's tickets for $2.70 each. Last Thursday, a total of $331.30 was collected from 89 movie watchers. How many of each type of ticket were sold on Thursday?

Answer 1

The Springfield Movie Theater last Thursday sold 65 adult tickets and 24 children's tickets.

Explanation:

1. Let's review the information provided to us to answer the problem correctly:

Price of adult ticket = US$ 4.10

Price of children ticket = US$ 2.70

Last Thursday total collection = US$ 331.30

Total movie watchers = 89

Number of adults = x

Number of children = y

2. How many of each type of ticket were sold on Thursday?

Let's build our equations system to answer the question, this way:

x + y = 89

4.10x + 2.70y = 331.30

Solving for x on the 1st equation:

x + y = 89

x = 89 - y

Replacing x on the 2nd equation and solving for y:

4.10x + 2.70y = 331.30

4.10 (89 - y) + 2.70y = 331.30

364.90 - 4.10y + 2.70y = 331.30

-1.40y = 331.30 - 364.90

-1.40y = - 33.60

y = -33.60/-1.40

y = 24

Solving for x:

x + y = 89

x + 24 = 89

x = 89 - 24

x = 65

Proof of x = 65 and y = 24

4.10x + 2.70y = 331.30

4.10 * 65 + 2.70 * 24 = 331.30

266.50 + 64.80 = 331.30

331.30 = 331.30

We proved that x = 65 and y = 24 are correct