Question

deb and luke go to the pi-rate entertainment store to purchase cds (c) and dvds (d). deb buys 3 dvds and 2 cds for $63 (before sales tax) at the same item prices, luke pays $46 for 1 dvd and 4 cds (before sales tax). write and solve a system of equations to determine the cost of 1 cd and dvd

Answer 1

Here's what we know:
D = 2C (A DVD has the same cost as 2 CDs)
2D + 2C = 45

Since we have a value for D, we can put that into our equation:
2(2C) + 2C = 45
4C + 2C = 45
6C = 45
C = 7.50

So a CD costs $7.50

Answer 2

We are given here the individual costs of DVD and CD as well as the total sales and the number of items sold on one day. To solve the number of DVDs and CDs sold each, we devise two independent linear equations:

(1) x + y = 39

(2) 4x + 7y = 204

x- number of DVDs; y - number of CDs

solving, x= 23 DVDs