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 $and the price of a sweatshirt is $.

Answer 1

Answer:

Cost of sweetshirt = 50 and cost of CD = 25

Step-by-step explanation:

Eric purchased three musics CDS and a sweatshirt

Let cost of CDs =c and cost of a sweatshirt =s

When after discount, 100 he pays means total cost =

$100=x*80%\\x = 125$

Hence we have

3c+s=125

Similarly when 120 is paid after 40% discount,

cost =$\frac{120}{100-40} *100=200$

i.e. $4c+2s=200$

Divide by 2

$2c+s=100$

Solving the two equations

$c=25\\s=125-3c\\=50$

Cost of sweetshirt = 50 and cost of CD = 25

Answer 2

If Eric received a 20% discount, his purchase would cost $125.  Similarly, if Neil had a 40% discount and his end price was $120, his original cost would be $200.  Therefore, letting c be the price of a CD and s the price of a sweatshirt:

3c+s=125
4c+2s=200

Subtracting double the first equation from the second, -2c=-50, so c=25.  Then, s+75=125, so s=50.  Thus, a CD costs $25 and a sweatshirt $50.