Question

A pet survey found that the ratio of dogsto onts Which proportion shows the number of dogs the number of cats is 140? A 2 dogs/5 cats = 56 dogs/ 140 catsB 2 dogs/ 5 cats = 28 dogs/ 140 catsC 2 dogs/5 cats = 140 dogs/ 350 catsD 2 dogs/ 5 cats = 140 cats/350 dogs

Answer 1

The ratio of dogs to cats is:

2 dogs/ 5 cats

--> 2 dogs for every 5 cats.

To find the number of dogs for which the number of cats is 140 we need to convert the proportion into a division by 140.

To find this proportion we need to multiply both parts (the number of dogs and the number of cats) by the same number.

We have two options that have 140 cats:

Option A:

`\frac{2\text{dogs}}{5\text{cats}}=\frac{56\text{dogs}}{140\text{cats}}`

And option B:

`\frac{2\text{dogs}}{5\text{cats}}=\frac{28\text{dogs}}{140\text{cats}}`

Not that we discard option C because it has 140 dogs, not cats.

And also discard option D because the number of cats should be in the denominator of the fraction, not the numerator.

Let's check if option A and B meet the condition of multiplying both numbers in the fraction by the same number:

And for option B we have:

As we can see, only in option B the proportion is kept by multiplying by the same number, and in option B the proportion is not kept because the numbers are not multiplied by the same number.

Answer: Option A