Sums in a Triangle
Date: 9/2/95 at 18:30:30 From: Anonymous Subject: Algebra Six numbered bottle caps are arranged in a triangle. The sum of the three corner numbers, 1+6+5, is three more than the sum of the remaining numbers. 1 4 3 6 2 5 How can you rearrange the bottle caps so that the sum of the corner number is: a. Twice the sum of the remaining numbers? b. The same as the sum of the remaining numbers?
Date: 9/6/95 at 11:32:48 From: Doctor Ken Subject: Re: Algebra Hello! To do these problems, we can write an equation. If I were given the first problem, the one that's already solved, I would use the variable X to represent the sum of the numbers on the corners, and write down the following equation: X + (X-3) = 1+2+3+4+5+6 = 21 The X is the numbers on the corners, and the X-3 is the other numbers (which add up to 3 less than X, hence the x-3). Then I could solve for X: 2X - 3 = 21 2X = 24 X = 12 So then all you'd have to do is fiddle around and try to find three numbers that add up to 12: 1+6+5 does fine, and so does 3+4+5 and a bunch of other solutions. How would you write an equation for the next problem? If the sum of the corner numbers is twice the sum of the remaining numbers, then the corner numbers are X and the other numbers are X/2, right? -Doctor Ken, The Geometry Forum
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