Question

The ratio of adult dogs to puppies at a park on Monday was 3:2. There were 12 puppies there that day. On Tuesday, 15 adult dogs were at the park. What is the difference between the number of adult dogs on Monday and Tuesday?

Answer 1

`3`

Explanation:

ratio of adult dogs to puppies: `3:2`

this means that the number of adult dogs is `3/2` times the number of puppies.

no. of puppies: `12`

`3/2 * 12 = 3 * 6 = 18`

there were `18` adult dogs in the park on Monday.

on Tuesday, there were `15`.

the difference between `18` and `15` is `18-15`, which is `3`.

(there were `3` fewer adult dogs on Tuesday than on Monday.)

Answer 2

`3`

Explanation:

There are two formats (as far as I know) for writing ratios

One is `3:2` and the other is in fraction FORMAT `3/2`
The latter is very useful for calculations.

Important: A ratio in fraction format is NOT a fraction of the whole (in most cases)

Using ratio in fraction format:

`color(brown)("For Monday - using first principles")`

`("adult dog")/("puppies")->3/2 =x/12`

For the shortcut method multiply both sides by 12
What follows is first principles:

`color(green)( 3/2color(red)(xx1)=x/12`

`color(green)( 3/2color(red)(xx6/6)=x/12`

`color(green)( color(white)("d")18/12color(white)("dd")=x/12`

`("adult dog")/("puppies")-> =18/12 larr" Actual counts"`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(brown)("Difference between adults for Monday and Tuesday")`

`"Monday's count " - " Tuesday's count"`

`color(white)("ddddd")18color(white)("ddddddd")-color(white)("ddddd")15color(white)("ddddddd") = 3`