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.
Accepted Solution
A:
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.