Question

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 remain the same. The last week of January there are 20 cats in the shelter. How many dogs are there?

Answer 1

Answer:

Step-by-step explanation:

If the ratio of dogs to cats is 49:28, as an actual ratio (fraction), this is

$\frac{d}{c}:\frac{49}{28}$

We can reduce that to make the numbers smaller without changing the ratio.  reducing gives us

$\frac{d}{c}:\frac{7}{4}$

We will use that ratio now to set up a proportion that involves a given number of cats and an unknown number of dogs.  Keeping dogs on top and cats on bottom,

$\frac{d}{c}:\frac{7}{4}=\frac{x}{20}$

Cross multiply to get

4x = 140 so

x = 35

According to the ratio of dogs to cats, if there are 20 cats, there will be 35 dogs.