Cinema tickets cost $110 for adults and $90 for kids. To a movie was sold in total 120 tickets for a total of $11640. How many adults watched the movie?

Let's define:

- $ x $ as the number of adults.
- $ y $ as the number of kids.

From the problem, we have two equations:

1. The total number of tickets sold: 
   \[
   x + y = 120
   \]
2. The total cost of the tickets sold: 
   \[
   110x + 90y = 11640
   \]

Now we solve this system of equations.

### Step 1: Solve the first equation for $ y $
\[
y = 120 - x
\]

### Step 2: Substitute $ y = 120 - x $ into the second equation
\[
110x + 90(120 - x) = 11640
\]

### Step 3: Simplify the equation
\[
110x + 90 \times 120 - 90x = 11640
\]
\[
110x + 10800 - 90x = 11640
\]
\[
20x + 10800 = 11640
\]

### Step 4: Solve for $ x $
\[
20x = 11640 - 10800
\]
\[
20x = 840
\]
\[
x = \frac{840}{20} = 42
\]

Thus, $ x = 42 $, meaning 42 adults watched the movie.

Would you like further details or have any questions?

Here are 5 related questions:
1. How many kids watched the movie?
2. What would the total revenue be if all tickets were sold to adults?
3. How many tickets need to be sold if only kids attend, to make $11,640?
4. What is the average cost per ticket sold in this scenario?
5. What happens if the adult ticket price increases by $10?

**Tip:** When solving systems of equations, substitution is a helpful method when one equation can easily be expressed in terms of one variable.

Find out how many adults watched the movie when 120 cinema tickets were sold for a total of $11,640. This problem uses algebraic methods, including solving a system of linear equations by substitution, ideal for students in Grades 6-8.

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