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7 cats and 3 dogs weigh as much as 4 monkeys. 1 monkey weighs as much as 1 cat and 1...
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This is an exercise in adding equations. So c, d, and m for cat, dog and monkey leads us to:
1) 7c + 3d = 4m
2) 1c + 1d = 1m
Adding these 2 equations gives:
3) 8c + 4d = 5m
Eight cats plus four dogs weighs the same as 5 monkeys. But by eq. 2, a monkey weighs as much as a cat and dog, so we can eliminate monkeys by substituting eq. 2 for m in eq. 3:
4) 8c + 4d = 5(1c + 1d)
5) 8c + 4d = 5c + 5d
6) 3c = 1d
So 3 cats weigh as much as a dog! If you substitute this value into eq. 2, you'll see also that a monkey weighs 4 cats.
Posted by enotechris on January 29, 2009 at 6:25 AM (Answer #1)
Let's break this problem into simultaneous equations:
7c+3d=4m - eqn 1
1c+1d=1m - eqn 2
Multiply eqn 2 by three
3c+3d=3m- eqn 3
Subtract eqn 3 from eqn 1
4c=m -eqn 4
Sub. eqn 4 to eqn 2
Thus, 3 cats equal 1 dog
Posted by revolution on July 31, 2010 at 10:33 PM (Answer #2)
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