Question

3) A puppy store has 30 dogs in total, some are largebreed and some are miniature breed. The ratio of largeto miniature dogs in the store is 2:3. How many largebreed puppies are there?

Answer 1

Let:

x = number of large breed dogs

y = number of miniature breed dogs

The puppy store has 30 dogs in total, so:

`x+y=30`

The ratio of large to miniature dogs in the store is 2:3. so:

`2\colon3=(2)/(3)=(x)/(y)`

Let:

`\begin{gathered} (x)/(y)=(2)/(3)_{\text{ }}(1)_{} \\ x+y=30_{\text{ }}(2) \end{gathered}`

From (1):

`x=(2)/(3)y_{\text{ }}(3)`

Replace (3) into (2):

`\begin{gathered} (2)/(3)y+y=30 \\ (5)/(3)y=30 \\ y=18 \end{gathered}`

Replace the value of y into (3):

`\begin{gathered} x=(2)/(3)(18) \\ x=12 \end{gathered}`

Answer:

There are 18 large breed puppies and there are 12 miniature breed puppies