Hat sizes are determined by measuring the circumference of one's head in either inches or centimeters. Use ratio and Proportion to complete the following table.
Hat Size:
6 and 7/8
Head Circumference (to the nearest 1/5 in):
21 and 3/5
Head Circumference (to the nearest cm) 55
Hat Size:
?
Head Circumference (to the nearest 1/5 in):
?
Head Circumference (to the nearest cm)
62
Make sure to keep the same denominator for Hat Size and Head Circumference (to the nearest 1/5 in)
55/S = (21 3/5) / (6 7/8).
Divide 21 3/5 by 6 7/8:
55/S = 3.142/1
Solve for S
S = 55/3.142 = 17.5 cm = 6 4/5 in. = Size of hat.
C = 55 cm = (55/2.54) in = 21.6 in. =
21 3/5 in
62/S = (21 3/5) /(6 7/8)
S = 19.74 cm = (19.74/2.54) in =
7.8 in = 7 4/5 in.
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.