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Slush Shack

Math brain teasers require computations to solve.


Puzzle ID:#49988
Fun:*** (2.47)
Difficulty:*** (2.91)
Submitted By:eighsseAus******




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 x-large (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 x-large, 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 much-below-average 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 best-selling size -- they sold exactly 4 times as many as smalls! -- followed by large, then x-large, 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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Nov 17, 2013

Quite challenging and lots of fun for those who enjoy math puzzles. Well done!
Nov 17, 2013

Thanks, my friend. Good to know my teaser is being enjoyed by a fellow math fan.
Jul 22, 2014

a great math teaser! no choice, had to use excel to figure this one out

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