Let:
x = number of large breed dogs
y = number of miniature breed dogs
The puppy store has 30 dogs in total, so:
[tex]x+y=30[/tex]The ratio of large to miniature dogs in the store is 2:3. so:
[tex]2\colon3=\frac{2}{3}=\frac{x}{y}[/tex]Let:
[tex]\begin{gathered} \frac{x}{y}=\frac{2}{3}_{\text{ }}(1)_{} \\ x+y=30_{\text{ }}(2) \end{gathered}[/tex]From (1):
[tex]x=\frac{2}{3}y_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} \frac{2}{3}y+y=30 \\ \frac{5}{3}y=30 \\ y=18 \end{gathered}[/tex]Replace the value of y into (3):
[tex]\begin{gathered} x=\frac{2}{3}(18) \\ x=12 \end{gathered}[/tex]Answer:
There are 18 large breed puppies and there are 12 miniature breed puppies
