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

The correct answer is D. 5 scarves and 10 hats

Step-by-step explanation:

1. Let's review the information given for answering the question correctly:

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

2. Let's find the number of scarves and hats that Zahra can knit to meet her goal

Answer A

10 scarves and 5 hats

200 * 10 + 5 * 150 = 2,000 + 750 = 2,750

2,750 exceeds the amount of yarn Zahra has.

Answer B

7 scarfs and 7 hats are less items than the 15 Zahra wants to knit

Answer C

6 scarves and 11 hats

200 * 6 + 11 * 150 = 1,200 + 1,650 = 2,850

2,850 exceeds the amount of yarn Zahra has.

Answer D

5 scarves and 10 hats

200 * 5 + 10 * 150 = 1,000 + 1,500 = 2,500

This option fulfills both conditions of inequality:

*. Minimum of 15 items

*. Less than 2,640 yards of yarn

answer:

step-by-step explanation:

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: