Maria spent the day working at a DVD shop.  They run a sale with $10 DVDs and $12 DVDs.  Her boss wants to know the total number of $12 DVDs they sold.  500 customers bought DVDs but she doesn’t want to go through all the receipts.  If she knows that they sold $5,750, how many did they sell?

Let's break down the problem:

- Let $ x $ be the number of $10 DVDs sold.
- Let $ y $ be the number of $12 DVDs sold.

We know two things:
1. The total number of DVDs sold is 500.
   \[
   x + y = 500
   \]
2. The total revenue from the DVDs is $5,750.
   \[
   10x + 12y = 5750
   \]

Now, we have a system of linear equations:
\[
\begin{aligned}
1. \quad & x + y = 500, \\
2. \quad & 10x + 12y = 5750.
\end{aligned}
\]

### Solving the system of equations:

1. Solve the first equation for $ x $:
   \[
   x = 500 - y
   \]

2. Substitute $ x = 500 - y $ into the second equation:
   \[
   10(500 - y) + 12y = 5750
   \]
   \[
   5000 - 10y + 12y = 5750
   \]
   \[
   2y = 5750 - 5000
   \]
   \[
   2y = 750
   \]
   \[
   y = \frac{750}{2} = 375
   \]

So, Maria's shop sold **375** $12 DVDs.

### Verifying the solution:
- If $ y = 375 $, then $ x = 500 - 375 = 125 $.
- Calculate the total revenue:
  \[
  10(125) + 12(375) = 1250 + 4500 = 5750
  \]
  
The calculation checks out, so the answer is correct.

Would you like more details on the steps, or do you have any other questions?

---

Here are 8 related questions:
1. How many $10 DVDs were sold?
2. What would the total revenue be if all DVDs were sold at $12 each?
3. How many DVDs would need to be sold to reach $10,000 in revenue?
4. What is the average price of the DVDs sold?
5. If the shop increases the price of $10 DVDs to $11, how does that affect the total revenue?
6. How many $12 DVDs would need to be sold to reach $6,000 in revenue?
7. If a customer bought one of each DVD, what would be the total cost?
8. What is the ratio of $10 DVDs to $12 DVDs sold?

**Tip:** When dealing with linear equations, substituting one equation into another is an effective method to solve for unknowns.

Learn how to solve a DVD sales problem where Maria needs to determine the number of $12 DVDs sold. Includes step-by-step calculations using linear equations. Suitable for students in Grades 7-9.

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