Question

A resale stores having a sale on DVDs and cds. DVDs cost $7 and CDs cost $4. on one day, the store made $211 from DVD and CD sales and so the total of 40 times. Write a system of equations then solve to find how many DVDs and CDs were sold show both the equations and the solution

Answer 1

To solve for the number of DVDs and CDs sold, two equations were set up: 7D + 4C = 211 and D + C = 40. By substituting D with (40 - C) in the first equation and solving, the store sold 17 DVDs and 23 CDs.

Step-by-step explanation:

To find out how many DVDs and CDs were sold, we can set up two equations based on the information given.

Let D be the number of DVDs sold and C be the number of CDs sold. Since DVDs cost $7 each and CDs cost $4 each, the total money made from selling these can be represented by the equation:

7D + 4C = 211

Additionally, we are told that a total of 40 items were sold. This gives us another equation:

D + C = 40

We now have a system of linear equations:

7D + 4C = 211

D + C = 40

To solve this, we can use the substitution or elimination method. In this case, we can isolate D in the second equation to get D = 40 - C and substitute this into the first equation.

Substitute D in the first equation:

7(40 - C) + 4C = 211

Now, solve for C:

280 - 7C + 4C = 211

-3C = 211 - 280

-3C = -69

C = 23

Having found C, we substitute it back into the second equation to find D:

D + 23 = 40

D = 40 - 23

D = 17

The store sold 17 DVDs and 23 CDs.