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.
