Question

Josiah is knitting hats as gifts. The pattern he is using is for the baby with a 14 inch head circumference and it says to use 36 stitches. he knows the number of stitches is proportional to head circumference and wants to knit a hat in a larger size for his baby sister. Her head circumference is 50 centimeters. How many stitches should he use? Round to the nearest number.

Answer 1

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.