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

Answer:

Weight of dog: 34 pounds,

Weight of cat: 12 pounds.

Step-by-step 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:

$3c-2=c+22$

$3c-c-2=c-c+22$

$2c-2=22$

$2c-2+2=22+2$

$2c=24$

$\frac{2c}{2}=\frac{24}{2}$

$c=12$

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.