select the correct answer.\nzahra is knitting items to sell at a craft fair. she has a total of 2,640 yards…

select the correct answer.\nzahra 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.\nthis system of inequalities represents this situation, where x is the number of scarves and y is the number of hats.\n200x + 150y ≤ 2,640\nx + y ≥ 15\nhow many scarves and hats can zahra knit to meet her goal?\na. 10 scarves and 5 hats\nb. 7 scarves and 7 hats\nc. 6 scarves and 11 hats\nd. 5 scarves and 10 hats
Answer
Explanation:
Step1: Check option A
For (x = 10) and (y=5), first check (200x + 150y): (200\times10+150\times5=2000 + 750=2750>2640), so option A does not satisfy (200x + 150y\leq2640).
Step2: Check option B
For (x = 7) and (y = 7), (x + y=7 + 7=14<15), so option B does not satisfy (x + y\geq15).
Step3: Check option C
For (x = 6) and (y = 11), (200x+150y=200\times6 + 150\times11=1200+1650 = 2850>2640), so option C does not satisfy (200x + 150y\leq2640).
Step4: Check option D
For (x = 5) and (y = 10), (200x+150y=200\times5+150\times10=1000 + 1500=2500\leq2640) and (x + y=5 + 10=15\geq15).
Answer:
D. 5 scarves and 10 hats