https://file.aiquickdraw.com/mathbot/file/1727461600784sxbhq2pj.jpg

The problem shown in the image is about solving how many child tickets were sold, given the total sales and ticket prices for both child and adult tickets.

Here’s a breakdown of the given information:

- Child admission price: $5.70
- Adult admission price: $9.80
- Total tickets sold: 149
- Total sales: $1078.90

Let $ x $ represent the number of child tickets sold and $ y $ represent the number of adult tickets sold. We have the following system of equations:

1. $ x + y = 149 $ (total number of tickets sold)
2. $ 5.70x + 9.80y = 1078.90 $ (total sales equation)

We can solve this system of equations step by step:

### Step 1: Solve for $ y $ in the first equation
From $ x + y = 149 $, solve for $ y $:
\[ y = 149 - x \]

### Step 2: Substitute $ y = 149 - x $ into the second equation
Substitute into the total sales equation:
\[ 5.70x + 9.80(149 - x) = 1078.90 \]

### Step 3: Simplify and solve for $ x $
Let’s expand and solve for $ x $:
\[
5.70x + 9.80(149) - 9.80x = 1078.90
\]
\[
5.70x + 1460.20 - 9.80x = 1078.90
\]
\[
-4.10x + 1460.20 = 1078.90
\]
\[
-4.10x = 1078.90 - 1460.20
\]
\[
-4.10x = -381.30
\]
\[
x = \frac{-381.30}{-4.10} = 93
\]

So, 93 child tickets were sold.

### Step 4: Verify by calculating the number of adult tickets
Now, substitute $ x = 93 $ into the first equation:
\[
y = 149 - 93 = 56
\]

### Step 5: Check the total sales
Now check if this satisfies the total sales:
\[
5.70(93) + 9.80(56) = 530.10 + 548.80 = 1078.90
\]

The solution is correct! 93 child tickets and 56 adult tickets were sold.

Would you like further clarification, or do you have any additional questions?

Here are five related questions you might find interesting:
1. What would happen to the solution if child ticket prices increased by 20%?
2. How would the total sales change if 20 more adult tickets were sold?
3. What is the percentage of child tickets sold compared to the total?
4. Can you solve this system using substitution or elimination methods? 
5. How would you approach the problem if the total number of tickets sold wasn’t given?

**Tip:** When solving word problems, always define your variables clearly and set up equations based on the given relationships.

At the movie theater, child admission is $5.70 and adult admission is $9.80. On Sunday, 149 tickets were sold for a total of $1078.90. How many child tickets were sold?

Solve a real-world problem involving movie ticket sales where child tickets are $5.70, adult tickets are $9.80, and 149 total tickets were sold for $1078.90. Learn how to set up and solve the system of linear equations step by step.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation