Question

Eric purchased three music CDs and a sweatshirt from a band's online store and received a 20% discount. He paid $100 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 four music CDs and two sweatshirts for $120. Assuming that the actual prices of the music CDs and the sweatshirts are unchanged, the price of a music CD is $_____
a. 20.
b. 25.
c. 30.
d. 50.

and the price of a sweatshirt is $_______.

a. 20.
b. 25.
c. 30.
d. 50.

Answer 1

The correct answers are:

B) $25; and

D) $50.

Explanation:

Eric got a 20% discount. This means he paid 100%-20% = 80% of the retail value.

Let C represent the cost of CDs and S represent the cost of sweatshirts. For Eric's purchase, we have the equation:

0.8(3C+S) = 100

Using the distributive property, we have

0.8(3C) + 0.8(S) = 100

2.4C + 0.8S = 100

Neil got a 40% discount; this means he paid 100%-40% = 60% of the retail value. We have the following equation for him:

0.6(4C+2S) = 120

Using the distributive property, we have:

0.6(4C)+0.6(2S) = 120

2.4C + 1.2S = 120

This gives us the system:

$\left \{ {{2.4C+0.8S=100} \atop {2.4C+1.2S=120}} \right.$

Since the coefficient of C is the same in each equation, we will eliminate this variable. We do this by subtracting the equations:

$\left \{ {{2.4C+0.8S=100} \atop {(2.4C+1.2S=120)}} \right. \\ \\-0.4S=-20$

We divide both sides by -0.4:

-0.4S/-0.4 = -20/-0.4

S = 50

Each sweatshirt is $50.

We will substitute this into the first equation:

2.4C+0.8(50) = 100

2.4C + 40 = 100

Subtract 40 from each side:

2.4C+40-40 = 100-40

2.4C = 60

Divide each side by 2.4:

2.4C/2.4 = 60/2.4

C = 25

Each CD is $25.

Answer 2

First, we derive the system of linear equations that would best represent the given above. That is,
                                0.8(3x + y) = 100
                                0.6(4x + 2y) = 120
where x and y are the prices of both CD and sweatshirt, respectively. Solving the equation gives an answer of,
                                  x = 25 an y = 50
Thus, each CD costs $25 and each sweathirt is $50. The answers are first, letter B and second, Letter D.