find the number of teeth that have touched after each full turn of the small gear. turns large gear teeth…

Explanation:

Step1: Identify the ratio

The ratio of large - gear teeth to small - gear teeth is constant. It's $\frac{12}{8}=\frac{3}{2}$.

Step2: Calculate for 3 turns of large gear

For 3 turns of the large gear with 36 teeth, let the number of teeth of the small gear be $x$. Since the ratio $\frac{36}{x}=\frac{3}{2}$, we cross - multiply: $3x = 36\times2$. Then $x=\frac{36\times2}{3}=24$.

Step3: Calculate for 4 turns of large gear

For 4 turns of the large gear with 48 teeth, let the number of teeth of the small gear be $y$. Using the ratio $\frac{48}{y}=\frac{3}{2}$, cross - multiply: $3y = 48\times2$. Then $y=\frac{48\times2}{3}=32$.

Answer:

24, 32