At a garage sale, the prices of all the items sold were different. The

Responding to a pm:

Prices of all items are different. Think of putting them on a list in decreasing order.

"the price of a DVD player sold was the 29th highest price as well as the 37th lowest price among all the prices of all the items sold"
- So a DVD player is 29th on the list and 37th from bottom. So it has another 36 items under it. This means there are a total of 29 + 36 = 65 items on the list.

Now consider doing the same for only the radios.
"If the price of a radio sold at the garage sale was the 15th highest price as well as the 20th lowest price among the prices of the radios sold"
- So a radio is 15th on the list and has 19 other radios under it. So there are a total of 15+19 = 34 radios.

This means we have 65 - 34 = 31 radios.