Question

FABRIC You can spend at most $60 on lace. Cotton lace is $2 per yard and linen lace is $3 per yard. Write an inequality for the amounts of lace you can buy. Can you buy 12 yards of cotton lace and 15 yards of linen lace? Explain. ​

Answer 1

Answer:

2c + 3l ≤ 60

No

Step-by-step explanation:

Let's say you buy c yards of cotton lace and l yards of linen lace. The cotton lace will cost $2 per yard, and for c yards, you have to pay $2 c times, coming to a total of 2*c for the cotton lace. For the linen lace, you'd have to pay 3*l for l yards. The total amount of lace is thus equal to cotton lace cost + linen lace cost = 2c + 3l.

Total amount needs to be less than or equal to 60 (at most 60), so total amount = 2c + 3l ≤ 60

We can then plug our values of cotton and linen lace into our equation

12 yards of cotton lace, 15 yards of linen lace

2c + 3l ≤ 60

2(12) + 3(15) ≤ 60

24 + 45 ≤ 60

69 ≤ 60

This is false, so you cannot buy these amounts of lace.