A puppy and two cats together weigh 24 pounds. the puppy and the larger cat together weigh exactly twice as much as the smaller cat, and the puppy and the smaller cat together weigh exactly the same as the larger cat. How many pounds does the puppy weigh?

Accepted Solution

Answer:Puppy = 4 poundsStep-by-step explanation:Let's think that the puppy is P, the larger cat is K and the smaller cat is C. We have the next system of equations:[tex]P+C+K=24[/tex][tex]P+K=2C[/tex][tex]P+C=K[/tex]Solving it we have:[tex]P+C+K=24[/tex][tex]K+K=24[/tex][tex]2K=24[/tex][tex]K=\frac{24}{2}=12[/tex]Now with searching for the value of C:[tex]P+C+K=24[/tex][tex]C+2C=24[/tex][tex]3C=24[/tex][tex]C=\frac{24}{3}=8[/tex]Finally P is:[tex]P+C+K=24[/tex][tex]P+8+12=24[/tex][tex]P+20=24[/tex][tex]P=24-20=4[/tex]Then the puppy is 4 pounds, the smaller cat is 8 pounds and the larger cat is 12 pounds.