Question

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

65 adult tickets and 24 children tickets were sold

Solution:

Let "a" be the number of adult tickets sold

Let "c" be the number of children tickets sold

Cost of 1 adult ticket = $ 4.10

Cost of 1 children ticket = $ 2.70

Last Thursday, a total of $331.30 was collected from 89 movie watchers

Number of movie watchers = 89

number of adult tickets sold + number of children tickets sold = 89

a + c = 89

c = 89 - a ----------- eqn 1

They collected a total of $ 331.30

Therefore, we frame a equation as:

number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = 331.30

`a * 4.10 + c * 2.70 = 331.30`

4.1a + 2.7c = 331.3 ------ eqn 2

Substitute eqn 1 in eqn 2

4.1a + 2.7(89 - a) = 331.3

4.1a + 240.3 - 2.7a = 331.3

Combine the like terms

1.4a = 331.3 - 240.3

1.4a = 91

a = 65

Substitute a = 65 in eqn 1

c = 89 - 65

c = 24

Thus 65 adult tickets and 24 children tickets were sold