# 7 cats and 3 dogs weigh as much as 4 monkeys. 1 monkey weighs as much as 1 cat and 1 dog. How many cats weigh as much as one dog?

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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.

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

1c+1d=4c 3c=1d//

Thus, 3 cats equal 1 dog