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?

1. Jezebel
Zahra can knit (D) 5 scarves and 10 hats to meet her goal.
Given information:
• The total amount of yarn Zahra has = 2,640 yards
• Amount of yarn per scarf Zahra uses = 200 yards
• Amount of yarn per hat Zahra uses = 150 yards
• Zahra wants to knit a minimum of 15 items
System of inequalities:
• 200x + 150y ≤ 2,640
• x + y ≥ 15
To find the number of scarves and hats that Zahra can knit to meet her goal:
(A) 10 scarves and 5 hats –
• 10 scarves and 5 hats
• 200 × 10 + 5 × 150 = 2,000 + 750 = 2,750
• 2,750 exceeds the amount of yarn Zahra has.
(B) 7 scarves and 7 hats –
• 7 scarves and 7 hats are fewer items than the 15 Zahra wants to knit.
(C) 6 scarves and 11 hats –
• 6 scarves and 11 hats
• 200 × 6 + 11 × 150 = 1,200 + 1,650 = 2,850
• 2,850 exceeds the amount of yarn Zahra has.
(D) 5 scarves and 10 hats –
• 5 scarves and 10 hats
• 200 × 5 + 10 × 150 = 1,000 + 1,500 = 2,500
This option fulfills both conditions of inequality:
1. Minimum of 15 items
2. Less than 2,640 yards of yarn
Therefore, Zahra can knit (D) 5 scarves and 10 hats to meet her goal.