To determine the hat size, we can use the ratio and proportion method.
Step 1: Compare the given values for the first hat size:
Hat Size: 6 and 7/8
Head Circumference: 21 and 3/5 inches
Step 2: Set up a proportion using the given values:
(Hat Size 1)/(Head Circumference 1) = (Hat Size 2)/(Head Circumference 2)
Let's call the second hat size and head circumference as Hat Size 2 and Head Circumference 2, respectively.
6 and 7/8 / 21 and 3/5 = Hat Size 2 / Head Circumference 2
Step 3: Solve for Hat Size 2:
Multiply both sides of the equation by Head Circumference 2:
Head Circumference 2 * (6 and 7/8) / (21 and 3/5) = Hat Size 2
Now we can substitute the given values for the second set of measurements:
Head Circumference 2 = 62 inches
Head Circumference 2 = 62 inches * (21 and 3/5) / (6 and 7/8)
To keep the same denominator (1/5) for the head circumference, we convert all measurements to fifths:
Head Circumference 2 = (62 * 5) * (21 * 5 + 3) / (6 * 5 + 7)
Simplifying the equation:
Head Circumference 2 = (310) * (108) / (37)
Head Circumference 2 = (33528) / (37)
Now, converting back to a mixed number:
Head Circumference 2 = 906 and 6/37 inches
Therefore, the Hat Size for the given Head Circumference of 62 inches is approximately 906 and 6/37 inches.