Yarn, Yarn and More Yarn – The Problems
December 22, 2008
Every year, during the holiday season, Mary knits gifts for several of her relatives. This year, she plans to make a hat for her cousin, a scarf and hat for her grandmother, two pairs of socks for her grandfather, two hats and a scarf for her mother, and a hat and two pairs of socks for her father. Each hat requires 1 ball of yarn, each scarf requires 3 balls of yarn and each pair of socks requires 1.5 balls of yarn. What is the minimum number of balls of yarn Mary must have to complete all the knitted gifts she intends to make?
After completing the hats, scarves and socks, Mary decides to make a very special holiday blanket. This blanket requires 1300 yards of yarn. Two-hundred of these yards should be one color, 800 yards should be a second color, and the remaining should be a third color. Unfortunately, she used up all of the yarn she had purchased for the gifts she made earlier, so she heads to the craft store to buy more yarn. The balls of yarn sold at her local craft store contain 150 yards of yarn. If yarn is only sold in whole balls, how many balls of yarn will she need to complete this project?
After completing the projects mentioned in the previous questions, balls of yarn went on sale at the local craft store. This prompted Mary to buy yarn for next year’s gifts. Mary bought 18 balls of yarn at the sale. She will make at least one hat, one scarf and one pair of socks from this yarn. If she only uses the 18 balls of yarn purchased at the sale and doesn't want to have any yarn left over, what is the largest number of scarves she can knit?
The solutions to this week's problems will be posted in the archive on Monday, December 29nd, 2008.