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?
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.