Final answer:
Ayana needs a total of 5/12 yards of blue fabric for each scarf when making 6 scarves from a total of 10 yards of fabric, which includes both blue and purple fabric.
Step-by-step explanation:
Ayana is making 6 scarves that each require 1 1/4 yards of purple fabric and she will use a total of 10 yards of fabric in all. To determine how many yards of blue fabric are needed for each scarf, we need to solve a two-step equation.
First, we calculate the total amount of purple fabric used for all the scarves by multiplying the amount needed for one scarf by the number of scarves:
- 1 1/4 yards per scarf × 6 scarves = 7 1/2 yards of purple fabric
Next, we subtract the total amount of purple fabric from the total amount of fabric to find the amount of blue fabric used:
- 10 yards total - 7 1/2 yards of purple fabric = 2 1/2 yards of blue fabric in total
To find the amount of blue fabric per scarf, we divide the total amount of blue fabric by the number of scarves:
- 2 1/2 yards of blue fabric ÷ 6 scarves = 5/12 yards of blue fabric per scarf