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Weighing Kittens - posted March 4, 2002My neighbor, George, owns seven kittens. The three oldest kittens are Liberty, Charlie and Alexander. The sum of their weights equals the sum of the weights of the four younger kittens (Sassy, Moonlight, Bubba and Randy).
Alexander weighs 2 oz. more than Charlie, who in turn weighs 6 oz. more than Liberty.
Bubba weighs 12 oz. more than Randy, who is 3 oz. more than Moonlight and 13 oz. more than Sassy.
Charlie and Bubba are almost the same weight, but Charlie is the heavier of the two.
If the kittens' weights are all whole ounces, what is the least that each kitten could weigh and still meet all of the given requirements?
If you represent each kitten's weight by its first initial and make as many equations as possible from the information given in the problem, you could try to write L + C + A all in terms of C and write S + M + B + R all in terms of B.
Once you have a statement in terms of C and B, there are a couple of different ways that you can figure out what C or B might be. Since you know that C is a little bigger than B (since Charlie and Bubba are almost the same weight, but Charlie is heavier), you can figure out some reasonable possibilities to try. Or you could actually let C equal B plus a little bit, say D (for the difference). Now C = B + D.
If you decide to stick with C and B, look carefully at the statement you ended up with. When you know that you're going to have to make guesses and check them, knowing that the answer has to be divisible by a certain number can dramatically reduce the range of possibilities.
If you said that C = B + D, you should end up with a statement in terms of B and D. You know that D, the difference between them, has to be a small whole number.
When we put everything in terms of C and B, we got(C - 6) + C + (C + 2) = (B - 25) + (B - 15) + B + (B - 12)
We eventually got 3C - 4 = 4B - 52. This tells us that C is divisible by 4 and greater than 48 and that B is divisible by 3.
We found that Charlie's weight is 52 ounces.
There are two solutions shown below. Compare them to your own and tell us what you think - is yours like either one, or a bit different? Did anything about these solutions surprise you? Did you learn anything? Do you have any questions?
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