Question

A dog weighs two pounds less than three times the weight of a cat. The dog also weights twenty-two more pounds than the cat. Write and solve an equation to find the weights of the cat and the dog.

Answer 1

Weight of dog: 34 pounds,

Weight of cat: 12 pounds.

Explanation:

Let d represent weight of dog and c represent weight of cat.

We have been given that a dog weighs two pounds less than three times the weight of a cat.

3 times weight of cat:
`3c`

We can represent the given information in an equation as:

`d=3c-2...(1)`

We are also told that the dog also weights twenty-two more pounds than the cat. We can represent the given information in an equation as:

`d=c+22...(2)`

Equate both equations:

`3c-2=c+22`

`3c-c-2=c-c+22`

`2c-2=22`

`2c-2+2=22+2`

`2c=24`

`(2c)/(2)=(24)/(2)`

`c=12`

Therefore, the weight of cat is 12 pounds.

Substitute
`c=12` in equation (2)

`d=c+22`

`d=12+22`

`d=34`

Therefore, the weight of dog is 34 pounds.