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
2,342
1,737
2,921

Explanation:

Step1: Add the two equations

We have the system of equations:

$$\begin{cases} x + y = 3500 \\ x - y = 2342 \end{cases}$$

Adding the two equations together: $(x + y) + (x - y) = 3500 + 2342$.
Simplifying the left side: $x + y + x - y = 2x$.
Simplifying the right side: $3500 + 2342 = 5842$.
So we get $2x = 5842$.

Step2: Solve for x

To find $x$, divide both sides of the equation $2x = 5842$ by 2: $x=\frac{5842}{2}$.
Calculating the division: $\frac{5842}{2}=2921$.

Answer:

2,921