Question

Doris uses 8 square pieces of fabricto make one scarf. Each side of a square piece of fabric is 4 yard in length. Doris can buy large pieces of fabric that are 4 yard long and 2 yards wide. How many large pieces of fabric should she buy to make 7 scarves? Show your work.

Answer 1

To find out how many large pieces of fabric Doris needs to buy to make 7 scarves, we can start by determining the total amount of fabric she will need.

1. **Calculate the area of one square piece of fabric:**
Each side of a square piece of fabric is 4 yards long. Thus, the area of one square piece is:
\[
\text{Area} = \text{side} \times \text{side} = 4 \text{ yards} \times 4 \text{ yards} = 16 \text{ square yards}.
\]

2. **Calculate the number of square pieces needed for one scarf:**
Doris uses 8 square pieces of fabric to make one scarf. Therefore, the total area of fabric needed for one scarf is:
\[
\text{Total area for one scarf} = 8 \times \text{Area of one square piece} = 8 \times 16 \text{ square yards} = 128 \text{ square yards}.
\]

3. **Calculate the total area needed for 7 scarves:**
To find the total area needed for 7 scarves, we multiply the area needed for one scarf by 7:
\[
\text{Total area for 7 scarves} = 7 \times 128 \text{ square yards} = 896 \text{ square yards}.
\]

4. **Calculate the area of one large piece of fabric:**
Each large piece of fabric is 4 yards long and 2 yards wide. Thus, the area of one large piece is:
\[
\text{Area of one large piece} = 4 \text{ yards} \times 2 \text{ yards} = 8 \text{ square yards}.
\]

5. **Calculate the number of large pieces of fabric needed:**
To find the number of large pieces of fabric needed, we divide the total area required by the area of one large piece:
\[
\text{Number of large pieces needed} = \frac{\text{Total area for 7 scarves}}{\text{Area of one large piece}} = \frac{896 \text{ square yards}}{8 \text{ square yards}} = 112.
\]

Therefore, Doris should buy **112 large pieces of fabric** to make 7 scarves.