Question

Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.

x + y = 3,500

x – y = 2,342

Solve the system of equations. How many contemporary titles does Jarred have?

1,158
1,737
2,342
2,921

Answer 1

To solve the system of equations, we have the following:

1. \( x + y = 3500 \) (Equation 1)
2. \( x - y = 2342 \) (Equation 2)

We can use the method of elimination or substitution. Here, we can add both equations to eliminate \( y \):

Adding Equation 1 and Equation 2:

\[
(x + y) + (x - y) = 3500 + 2342
\]

This simplifies to:

\[
2x = 5842
\]

Now, divide both sides by 2:

\[
x = \frac{5842}{2} = 2921
\]

Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):

\[
2921 + y = 3500
\]

Subtracting 2921 from both sides gives:

\[
y = 3500 - 2921 = 579
\]

Thus, the solution to the system of equations is:

- Number of contemporary titles (\( x \)) = 2921
- Number of classic titles (\( y \)) = 579

Therefore, the number of contemporary titles Jarred has is **2,921**.