Question

Ayana is making six scarves That each require 1 1/4 yards of purple fabric and a certain amount of blue fabric. She will use 10 yards in all which equation can be used to determine how many yards of blue fabric be are needed for each scarf?

Answer 1

A simple algebraic equation can be utilized to solve this question. Ayana needs $\frac{5}{12}$ yards of blue fabric for each scarf.

Step-by-step explanation:

Step 1; Assume the amount of purple fabric to be x for each scarf and the amount of blue fabric required for each scarf to be y. It says a total of six scarves are needed. It is given that a total of 10 yards of fabric is used i.e. the total of purple fabric and the blue fabric. So we can create an equation for this. As 6 scarves are needed we substitute x and y as 6x and 6y.

Total fabric used= 6x + 6y = 10 yards.

Step 2; It is given that for each and every scarf 1$\frac{1}{4}$ yards of purple fabric is needed. So for 6 scarves a total of 6 * 1$\frac{1}{4}$ yards is needed. So 6x becomes 6 * 1$\frac{1}{4}$ yards.

6x = 6 * 1$\frac{1}{4}$ yards = 6 * $\frac{5}{4}$ = $\frac{30}{4}$ yards of purple fabric.

Step 3; Now we solve for the amount of blue fabric needed.

6y = 10 - $\frac{30}{4}$ = $\frac{40-30}{4}$ = $\frac{10}{4}$

But the $\frac{10}{4}$ yards is for 6 scarves to we divide it by 6 to get the material needed for a single scarf

y = $\frac{10}{4}$/6 = $\frac{10}{4}$ * $\frac{1}{6}$ = $\frac{10}{24}$ = $\frac{5}{12}$ yards = 0.4166 yards of blue fabric for each scarf.