Questions: (5) The first week of January, there are 49 dogs and 28 cats in an animal shelter. Throughout the month, the ratio of dogs to cats remains the same. The last week of January, there are 20 cats in the shelter. How many dogs are there?

(5) The first week of January, there are 49 dogs and 28 cats in an animal shelter. Throughout the month, the ratio of dogs to cats remains the same. The last week of January, there are 20 cats in the shelter. How many dogs are there?

Transcript text: (5) The first week of January, there are 49 dogs and 28 cats in an animal shelter. Throughout the month, the ratio of dogs to cats remains the same. The last week of January, there are 20 cats in the shelter. How many dogs are there?

Solution

Solution Steps

Step 1: Determine the Initial Ratio

The initial number of dogs and cats in the shelter is given as:

Dogs: \( D = 49 \)
Cats: \( C = 28 \)

The ratio of dogs to cats can be expressed as: \[ \text{Ratio} = \frac{D}{C} = \frac{49}{28} = \frac{7}{4} = 1.75 \]

Step 2: Calculate the Number of Dogs at the End of the Month

At the end of January, the number of cats in the shelter is: \[ C_{\text{end}} = 20 \]

To maintain the same ratio of dogs to cats, we can express the number of dogs at the end of the month as: \[ D_{\text{end}} = \text{Ratio} \times C_{\text{end}} = 1.75 \times 20 = 35.0 \]