230k views
3 votes
A movie theater has a seating capacity of 177.

The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults.
There are half as many adults as there are children.
If the total ticket sales was $ 1276, How many children, students, and adults attended?
______ Children attended?
______ Students attended?
______ Adults attended?

1 Answer

6 votes
Sure, here is the step-by-step working for the solution:

Given information:

Seating capacity of theater = 177
Ticket price for children = $5
Ticket price for students = $7
Ticket price for adults = $12
Number of adults = half the number of children
Total ticket sales = $1276
Let's represent the number of attendees with variables:

C: number of children
S: number of students
A: number of adults
From the given information, we can write the following equations:

A = 0.5C (since there are half as many adults as there are children)
C + S + A ≤ 177 (since the seating capacity of the theater is 177)
5C + 7S + 12A = 1276 (since the total ticket sales is $1276)
We can substitute the first equation into the third equation to get an equation with two variables:
5C + 7S + 12(0.5C) = 1276
Simplifying this, we get:
6.5C + 7S = 1276

Now we have two equations with two variables, so we can solve for C and S. We can isolate S in the second equation:
S ≤ 177 - C - A
S ≤ 177 - C - 0.5C
S ≤ 176.5 - 1.5C

We can substitute this inequality into the first equation:
6.5C + 7(176.5 - 1.5C) = 1276

Simplifying this, we get:
-0.5C = -46.5
C = 93

Substituting this value of C into the inequality for S:
S ≤ 176.5 - 1.5(93)
S ≤ 49.5

Now we can solve for A using the first equation:
A = 0.5C
A = 0.5(93)
A = 46.5, which we can round up to 47.

Therefore, the solution is:

93 children attended
49 students attended
47 adults attended
We can check that this solution is correct by verifying that the total ticket sales is $1276:
5(93) + 7(49) + 12(47) = 465 + 343 + 564 = 1276
User Rohit Ramani
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories