Final answer:
To knit a larger hat for his sister with a 50 cm head circumference, Josiah should use 51 stitches, after converting the circumference to inches and setting up a proportion with the original pattern.
Step-by-step explanation:
Josiah is knitting hats and wants to find out how many stitches to use for a larger hat, based on the knowledge that the number of stitches is proportional to head circumference.
The original pattern is for a baby with a 14-inch head circumference using 36 stitches. To adjust for his baby sister's head circumference of 50 centimeters, we first need to convert centimeters to inches, knowing that 1 inch equals 2.54 centimeters.
We start by dividing her head circumference in centimeters by 2.54 to convert it to inches:
50 cm ÷ 2.54 = 19.685 inches (approximately).
Next, we set up a proportion based on the original pattern:
14 inches/36 stitches = 19.685 inches/x stitches.
Solve for x (number of stitches for his sister's hat) by cross-multiplying and dividing:
14x = 36 × 19.685
14x = 708.66
x = 708.66 ÷ 14
x = 50.62 stitches.
Since Josiah cannot use a fraction of a stitch, he should round to the nearest number, resulting in 51 stitches for his baby sister's larger hat.