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 $.

Question

Mathematics

Golden

13 April, 06:38

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 $.

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Jonathan Lin · Answer 1

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.