Question

Zahra is knitting items to sell at a craft fair. She has a total of 2,640 yards of yarn. A scarf uses 200 yards of yarn, and a hat uses 150 yards. She wants to knit a minimum of 15 items. This system of inequalities represents this situation, where x is the number of scarves and y is the number of hats. 200x + 150y ≤ 2,640 x + y ≥ 15 How many scarves and hats can Zahra knit to meet her goal? A. 10 scarves and 5 hats B. 7 scarves and 7 hats C. 6 scarves and 11 hats D. 5 scarves and 10 hats

Answer 1

Zahra can knit a maximum of 7 scarves and a minimum of 8 hats to meet her goal.

Step-by-step explanation:

Mathematics - High School

To determine how many scarves and hats Zahra can knit to meet her goal, we need to solve the system of inequalities:

200x + 150y ≤ 2,640

x + y ≥ 15

Let's start with the second inequality, x + y ≥ 15. We can rewrite this equation as y ≥ 15 - x.

Now let's substitute this expression for y in the first inequality:

200x + 150(15 - x) ≤ 2,640

Simplifying, we have:

200x + 2250 - 150x ≤ 2,640

Combining like terms:

50x + 2250 ≤ 2,640

Subtracting 2250 from both sides:

50x ≤ 390

Dividing both sides by 50:

x ≤ 7.8

Since x represents the number of scarves Zahra can knit, she can knit a maximum of 7 scarves. Substituting this value into the second inequality, we have:

7 + y ≥ 15

Simplifying, we get:

y ≥ 15 - 7

y ≥ 8

Since y represents the number of hats Zahra can knit, she can knit a minimum of 8 hats. Therefore, Zahra can knit a maximum of 7 scarves and a minimum of 8 hats to meet her goal.

Answer 2

Zahra can knit 7 scarves and 7 hats to meet her goal of producing a minimum of 15 items and staying within her yarn limit of 2,640 yards.

Step-by-step explanation:

Zahra is knitting items to sell at a craft fair with a total of 2,640 yards of yarn. She can knit scarves using 200 yards of yarn each, and hats using 150 yards each. To meet her goal of knitting a minimum of 15 items, she must follow the system of inequalities: 200x + 150y ≤ 2,640 and x + y ≥ 15. To determine the number of scarves (x) and hats (y) she can make, we can look at the options provided.

• A. 10 scarves and 5 hats: (10*200) + (5*150) = 2,000 + 750 = 2,750 (exceeds the yarn limit)
• B. 7 scarves and 7 hats: (7*200) + (7*150) = 1,400 + 1,050 = 2,450 (meets the yarn limit, meets item count)
• C. 6 scarves and 11 hats: (6*200) + (11*150) = 1,200 + 1,650 = 2,850 (exceeds the yarn limit)
• D. 5 scarves and 10 hats: (5*200) + (10*150) = 1,000 + 1,500 = 2,500 (meets the yarn limit, exceeds the item count)

Option B with 7 scarves and 7 hats is the correct combination that meets both the yarn limit and the minimum item count. Thus, Zahra can knit 7 scarves and 7 hats to meet her goal.