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Slush Shack
Category:  Math 
Submitted By:  eighsse 
Fun:  (2.34) 
Difficulty:  (2.85) 
You have a small shack in a parking lot, out of which you sell slushes for a few hours a day. You sell them in 4 sizes: small (12 oz), medium (20 oz), large (32 oz), and xlarge (40 oz), and you charge $1.50, $2.25, $3.75, and $4.50 for each size, respectively. The cups cost you 3 cents for small, 5 cents for medium, 8 cents for large, and 10 cents for xlarge, and the slush ingredients cost you 6 cents per ounce. Today, you are having a special: with every slush purchased, the customer receives a coupon for a free small slush. You figure that this special will increase sales for the day, but that the losses (due to giving out free slushes in the future) will cut the profit down to a muchbelowaverage day. Your hope, though, is that it will help by drawing more regular customers in the long run. Your goal is to profit $20 even after the coupon losses. Through the day, medium was the bestselling size  they sold exactly 4 times as many as smalls!  followed by large, then xlarge, and finally small. At the end of the day, the profit (not accounting for the coupons) from your sales was $46.50. Did you make the $20 net profit goal?
(This is strictly profit of sale over purchase, not involving paying employees, bills, etc. Also, assume that the customers who use the coupons would not have returned if they didn't have the coupon. Therefore, the loss from a coupon is the cost for you to make the slush, not the price you would normally receive for it.)
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