MATH SOLVE

4 months ago

Q:
# 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+y≤20x+y≤20x≤5x≤5y≤8y≤85x+8y≤205x+8y≤2012x+6y≤20

Accepted Solution

A:

x+y<=20 is false, because it tries to correlate the amount of hats and scarfs with the time, without considering the time to knit each object

x<=5 is correct, he can at most make 5 hats for more he is missing yarn

y<=8 is correct, same reasoning but with scarfs

5x+8y<=20 is false, it compares the yarn requirements with the total time

12x+6y<=20 is correct, a corrected version of the first constraint which uses the worktime of each object essentially meaning "the time worked on all objects has to be less than the 20 hour time total"

so

x<=5

y<=8

12x+6y<=20

are correct

x<=5 is correct, he can at most make 5 hats for more he is missing yarn

y<=8 is correct, same reasoning but with scarfs

5x+8y<=20 is false, it compares the yarn requirements with the total time

12x+6y<=20 is correct, a corrected version of the first constraint which uses the worktime of each object essentially meaning "the time worked on all objects has to be less than the 20 hour time total"

so

x<=5

y<=8

12x+6y<=20

are correct