Question

Dakota is working furiously to knit scarves and beanies for a craft fair next weekend. Yesterday she completed 2 scarves and three beanies, using a total of 19 meters of yarn. The day before, she used 16 meters to knit 2 scarves and 2 beanies. Assuming Dakota is using the same pattern and type of yarn for each scarf and beanie, how much yarn does each project require?

Answer 1

Answer: Scarves require 5 meters of yarn and beanies require 3 meters of yarn.

Step-by-step explanation:

This can be solved by system of equations. Let's pick two variables, one to show the beanies called b and one to show the scarves called s. We know that using 19 meters total of yarn, she comleted t scarves and 3 beaines so 2s + 3b = 19. From the second piece of information we get 2s + 2b = 16.

Now we solve system of equations.

Let's use the elimination method.

1) 2s + 2b = 16

  2s + 3b = 19

2) Multiply equation one by -1

-2s - 2b = -16

2s + 3b = 19

3) Add equations

b = 3

4) Plug in b = 3 to one of the equations:
2(s) + 3(3) = 19

5) Solve for s

2s + 9 = 19

2s = 10

s = 5

Now we know the amount of yarn! Scarves require 5 meters of yarn and beanies require 3 meters of yarn.