Question

Jerome knits scarves and hats for charity. Scarves require 4 skeins of yarn, and hats require 2 skeins of yarn. Jerome has 24 skeins of yarn. Write a function to represent the combination of scarves and hats he can knit. Draw the graph of the function. Let 2 represent the number of scarves, and let y represent the number of hats.

Answer 1

A function to represent the combination of scarves and hats Jerome can knit, given his yarn constraints, is 4s + 2y ≤ 24. To graph this function, plot the points (0,12) and (6,0), draw a line through them, and shade below and to the left.

Step-by-step explanation:

To write a function representing the combination of scarves and hats Jerome can knit, let s represent the number of scarves, and y represent the number of hats. Since scarves require 4 skeins of yarn, and hats require 2 skeins, and Jerome has 24 skeins, the function will show the total skeins used by Jerome to be at most 24:

4s + 2y ≤ 24

To graph this function, convert the inequality into an equation to find the boundary line:

4s + 2y = 24

Here are steps to sketch the graph:

1. When s=0 (no scarves), y=24/2, y=12 (all yarn used for hats).
2. When y=0 (no hats), s=24/4, s=6 (all yarn used for scarves).
3. Plot these points as (0,12) and (6,0) on a graph.
4. Draw a straight line through these points; this is the boundary.
5. The area below and to the left of the line represents all the possible combinations of scarves and hats Jerome can knit.