Question

Mary is making some shirts for her school's drama department. The fabric store has 3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts. What length of fabric does Mary need to buy if she wants to sew 2 shirts?

Answer 1

The answer is 4 3/4 yards of the fabric.

This can be calculated using the proportion.
If the 3 1/6 yards of the fabric is enough for 1 1/3 shirts, how many yards are necessary of 2 shirts:
$3 \frac{1}{6} yards :1 \frac{1}{3}shirts =xyards:2shirts$

Let's express 3 1/6 as 19/6:
$3 \frac{1}{6} =3+ \frac{1}{6} = 3* \frac{6}{6}+ \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{18+1}{6} = \frac{19}{6}$

Similarly, 1 1/3 = 4/3:
$1 \frac{1}{3} =1+ \frac{1}{3} = 1* \frac{3}{3}+ \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{3+1}{3} = \frac{4}{3}$

Now, let's use this in the proportion:
$3 \frac{1}{6} yards :1 \frac{1}{3}shirts =xyards:2shirts$
$\frac{19}{6} : \frac{4}{3} = x:2$

Crossing the products:
$x* \frac{4}{3} =2* \frac{19}{6}$
⇒ $x* \frac{4}{3} = \frac{19}{3}$
⇒ $x = \frac{19}{3} : \frac{4}{3}$
$x= \frac{19}{3} * \frac{3}{4}$
⇒ $x = \frac{19}{4} = \frac{16+3}{4} = \frac{16}{4} + \frac{3}{4} =4+ \frac{3}{4} =4 \frac{3}{4}$

Therefore, Mary needs in total 4 3/4 yards of the fabric.

Answer 2

Answer:

The answer is 4 3/4 yards of the fabric.