You are probably familiar with the coupons from Bed, Bath, and Beyond that come in the mail, and never expire (If you didnt know that, now you do! It is true!). They can come in two forms: 20% off one single item, regardless of price, or $5 off a purchase of $15 or more. For simplicity sake, lets say you are going to Bed, Bath, and Beyond and you wish to purchase one single item. You enter the store with one of each coupon in hand.

1. Suppose the item you select costs $75 before any discounts. Calculate the final price if you use the 20% coupon.

2. For the same $75 item, calculate the final cost of the $5 coupon is used.

3. Considering the final prices in (a) and (b), which coupon will give the lower final price?

4. Repeat (a), (b), and (c) for a $17 item.

5. For what price does the 20% coupon give the same discount as the $5 coupon? Be sure to show your support with mathematical equations. Showing an answer works without showing how you got that answer will earn no credit.