Bedbugs and Beds
Date: 09/14/97 at 21:41:57 From: adi mulzer Subject: Bedbugs and Beds Please help me. I can't figure out this problem - I don't even know where to begin. The happy Holiday hotel is blessed with cheerful bedbugs. In each single bed you can find 7 bedbugs, and in each double bed 13 bedbugs. If there are 106 bedbugs in all, how many double beds are there? Could you please tell me how you got your answer? My teacher always wants me to show my work. Thank you! Adi Mulzer
Date: 09/15/97 at 09:12:18 From: Doctor Anthony Subject: Re: Bedbugs and Beds In this type of problem you should introduce letters to represent unknown quantities. This allows you to write down equations using the information given in the question. Finally, you solve the equations to find actual values for the unknown quantities. Let x = number of double beds and y = number of single beds. Then 13x + 7y = 106 13x = 106 -7y 106 - 7y x = ---------- 13 Now let y range through the values 1, 2, 3, .... until you find a value for 106-7y which is exactly divisible by 13. There are not many numbers between 13 and 106 that are multiples of 13, so the search will be easy. Multiples of 13 are 13, 26, 39, 52, 65, 78, 91, 104 values of 106-7y for y = 0, 1, 2, 3, ... are 106, 99, 92, 85, 78, ... The number 78 appears in both lists, so x = 78/13 = 6 y = 4 So there are 6 double beds and 4 single beds. (Check. Number of bugs = 13 x 6 + 7 x 4 = 106) -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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