Let's use algebra to represent the weights of the dog and the cat.
Let D represent the weight of the dog in pounds.
Let C represent the weight of the cat in pounds.
According to the information given:
1. The dog weighs two pounds less than three times the weight of a cat, so we can write this as an equation: D = 3C - 2.
2. The dog also weighs twenty-two pounds more than a cat, so we can write this as another equation: D = C + 22.
Now, we have a system of two equations:
1. D = 3C - 2
2. D = C + 22
To solve for the weights of the dog and the cat, we can set these two equations equal to each other since they both equal D:
3C - 2 = C + 22
Now, let's solve for C (the weight of the cat):
3C - C = 22 + 2
This simplifies to:
2C = 24
Now, divide both sides by 2 to find the value of C (the weight of the cat):
C = 24 / 2
C = 12
So, the weight of the cat is 12 pounds.
Now, we can find the weight of the dog using either of the two original equations. Let's use the second equation:
D = C + 22
D = 12 + 22
D = 34
So, the weight of the dog is 34 pounds.
Therefore, the dog weighs 34 pounds, and the cat weighs 12 pounds.