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: [tex]3c[/tex]
We can represent the given information in an equation as:
[tex]d=3c-2...(1)[/tex]
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:
[tex]d=c+22...(2)[/tex]
Equate both equations:
[tex]3c-2=c+22[/tex]
[tex]3c-c-2=c-c+22[/tex]
[tex]2c-2=22[/tex]
[tex]2c-2+2=22+2[/tex]
[tex]2c=24[/tex]
[tex]\frac{2c}{2}=\frac{24}{2}[/tex]
[tex]c=12[/tex]
Therefore, the weight of cat is 12 pounds.
Substitute [tex]c=12[/tex] in equation (2)
[tex]d=c+22[/tex]
[tex]d=12+22[/tex]
[tex]d=34[/tex]
Therefore, the weight of dog is 34 pounds.
