Question

Ronald is making hats and scarves for charity. He has enough yarn to make 5 hats and 8 scarves. It takes him 12 hours to knit a hat and 6 hours to knit a scarf; he has 20 hours to knit.

Let x represent the number of hats made. Let y represent the number of scarves made.

Which inequalities are among the constraints for this situation?

Select each correct answer.


x≤5

x+y≤20

5x+8y≤20

y≤8

12x+6y≤20

Answer 1

x ≤ 5

y ≤ 8

12x + 6y ≤ 20

Explanation:

First, x ≤ 5 is a constraint because Ronald has enough yarn to make 5 or less hats.

y ≤ 8 is also a constraint because Ronald has enough yarn to make 8 or less scarves.

Lastly, 12x + 6y ≤ 20 is a constraint because Ronald has 20 hours to knit, and it takes 12 hours to knit a hat and 6 hours for a scarf.