To find the number of centimeters in 1 inch, we start with the proportional relationship given:
\[ 6y = 15.24x \]
Here, \( y \) represents the number of centimeters in 1 inch (which we want to find) and \( x \) represents the number of inches.
We can rearrange the equation to isolate \( y \):
\[ y = \frac{15.24}{6} x \]
Since we are interested in the number of centimeters in 1 inch (where \( x = 1 \)), we substitute 1 for \( x \):
\[ y = \frac{15.24}{6} \]
Now, we calculate \( y \):
\[ y = 15.24 รท 6 = 2.54 \text{ centimeters} \]
Therefore, the number of centimeters in 1 inch is:
2.54 centimeters