Seven cats and 3 dogs weigh as much as 4 monkeys. One monkey weighs as much as 1 cat and 1 dog. How many cats weigh as much as 1 dog?
7c+3d = 4m
1m = 1c+1d
So,
4m = 4c+4d
7c+3d = 4c+4d
3c = d
To solve this problem, we need to set up a system of equations using the given information.
Let's represent the weight of a cat as 'C', the weight of a dog as 'D', and the weight of a monkey as 'M'.
From the first sentence, we know that:
7C + 3D = 4M ---(equation 1)
From the second sentence, we know that:
1M = 1C + 1D ---(equation 2)
We need to find how many cats (C) weigh as much as 1 dog (D). To do that, we can isolate either C or D in terms of the other variable.
Let's solve equation 2 for C:
C = 1M - 1D
Now we can substitute this value of C in equation 1:
7(1M - 1D) + 3D = 4M
Simplifying this equation gives us:
7M - 7D + 3D = 4M
7M - 4M = 7D - 3D
3M = 4D
Now, we know that 3M is equal to 4D. Since we want to find how many cats (C) weigh as much as 1 dog (D), we need to find the ratio of cats to dogs. We can set up the following equation:
C/D = 3/4
Therefore, 3 cats weigh as much as 4 dogs.