How Much Popcorn did Paul Sell?
Date: 01/28/2002 at 08:50:16 From: Melissa Subject: How much popcorn did he sell? Paul made $44.14 selling 27 items (beer and popcorn). If he made $1.22 selling popcorn and $2.62 selling beer, how many boxes of popcorn were sold? What I did... I said that x(1.22) + n(2.62) = 44.14 Then I said that x+n = 27 Then I divided 27 by 2 because he sold two items, and I got 13.5 So then I said that he couldn't sell half an item, so I made the pocorn 14 and the beer 13. 14(1.22) = 17.08 and 13(2.62) = 34.06 and 17.08+34.06 = 51.14, but that's too much because he only made $44.14. Help, please.
Date: 01/28/2002 at 10:04:39 From: Doctor Ian Subject: Re: How much popcorn did he sell? Hi Melissa, You've set up exactly the right equations, although, can I make a suggestion? Whenever you're working with dollars and cents, consider working with pennies, since then everything will be an integer. Integers are generally the easiest kind of number to work with. Note that you _could_ find the answer by trying other values for x and n. For example, when you set x = 14 and n = 13, you end up with too much money. Since beer is the more expensive item, you could get a smaller total by selling fewer beers and more popcorn, so you might set x = 15 and n = 12: 15(122) + 12(262) = 4974 which is still too big, but we're getting closer. If we keep increasing x and reducing n, we'll eventually get to the answer: 14(122) + 13(262) = 5114 15(122) + 12(262) = 4974 16(122) + 11(262) = 4834 . . __(122) + __(262) = 4414 But a reasonable question to ask is: Is there an easier way to find the answer? (One way of thinking about math is this: It's the study of finding easier ways to get answers. Which is why everyone places so much emphasis on it.) Let's look at your equations: 122x + 262n = 4414 x + n = 27 Dividing 27 by two would give you the average number of items sold, but that's not really what you're after. What you want to find is _exactly_ how many of each type that he sold. To do that, you need to find a set of values for x and n that make both equations true at the same time. If that concept doesn't make sense to you, you might want to take a look at The Idea behind Simultaneous Equations http://mathforum.org/dr.math/problems/laura.10.14.01.html If the concept makes sense, but you just don't know how to solve the equations, take a look at Substitution and Elimination http://mathforum.org/dr.math/problems/kathryn.01.13.02.html Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 01/28/2002 at 13:30:10 From: Melissa Subject: How much popcorn did he sell? Thanks! 19 popcorn and 8 beers :)
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