Question

Eric purchased three music CDs and a sweatshirt from a band's online store and received a 20% discount. He paid $56 for his purchase. The following week, the same store offered a 40% discount on all its products. Eric's friend Neil took advantage of the sale and bought one music CD and two sweatshirts for $48. Assuming that the actual prices of the music CDs and the sweatshirts are unchanged, how much was the band charging for each CD and sweatshirt?

Answer 1

By creating a system of equations from the purchases of Eric and Neil, we determine that the price of one music CD is $8 and the price of one sweatshirt is $34.

Step-by-step explanation:

To solve this problem, we need to establish a system of equations based on the information provided about Eric and Neil's purchases and apply the discounts they received. Let's denote the price of one music CD as C and the price of one sweatshirt as S. Eric purchased three music CDs and a sweatshirt at a 20% discount and paid $56, while Neil bought one music CD and two sweatshirts at a 40% discount for $48.

We can set up the two equations as follows:

1. Equation 1 (Eric's purchase): 3C + S - 0.20(3C + S) = $56
2. Equation 2 (Neil's purchase): C + 2S - 0.40(C + 2S) = $48

To solve these equations, we need to simplify and rearrange them:

1. 0.80(3C + S) = $56 becomes 2.4C + 0.8S = $56
2. 0.60(C + 2S) = $48 becomes 0.6C + 1.2S = $48

We can then multiply the second equation by 4 to equalize the coefficient of C and then subtract the first equation from the new second equation:

2.4C + 4.8S = $192 (after multiplying by 4) - 2.4C + 0.8S = $56

This simplifies down to 4S = $136, which means S = $34 for the sweatshirt. Plugging S back into either equation, we can solve for C to find that C = $8 for the music CD.