An animal shelter has cats and dogs available for adoption in a ratio of 3:5

. If there are 25 dogs available for adoption, how many cats are available? Use a tape diagram to help organize your thinking.(1 point)
cats

1 answer

To solve this problem using the ratio of cats to dogs, which is given as 3:5, we can break this down step by step.

  1. Understanding the Ratio:

    • The ratio 3:5 means that for every 3 cats, there are 5 dogs.
  2. Finding the Value of One Unit in the Ratio:

    • The total parts in the ratio (3 parts for cats + 5 parts for dogs) is 8 parts.
  3. Determining the Size of Each Part:

    • We know that there are 25 dogs available for adoption.
    • According to the ratio, the 5 parts correspond to the number of dogs.
    • Therefore, we divide the total number of dogs (25) by the number of dog parts (5): \[ \text{Value of one part} = \frac{25 \text{ dogs}}{5} = 5 \]
  4. Calculating the Number of Cats:

    • Since cats make up 3 parts in the ratio, we can find the number of cats by multiplying the value of one part by the number of cat parts: \[ \text{Number of cats} = 3 \times 5 = 15 \]
  5. Conclusion:

    • Therefore, there are 15 cats available for adoption.

Using a tape diagram, you could represent each part visually, drawing 3 sections labeled "cats" and 5 sections labeled "dogs," with each section corresponding to 5 animals. This visually reinforces that if there are 25 dogs (5 sections), then 3 sections equals 15 cats.