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:
[tex]3 \frac{1}{6} yards :1 \frac{1}{3}shirts =xyards:2shirts[/tex]
Let's express 3 1/6 as 19/6:
[tex]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} [/tex]
Similarly, 1 1/3 = 4/3:
[tex]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} [/tex]
Now, let's use this in the proportion:
[tex]3 \frac{1}{6} yards :1 \frac{1}{3}shirts =xyards:2shirts[/tex]
[tex] \frac{19}{6} : \frac{4}{3} = x:2[/tex]
Crossing the products:
[tex]x* \frac{4}{3} =2* \frac{19}{6} [/tex]
⇒ [tex]x* \frac{4}{3} = \frac{19}{3} [/tex]
⇒ [tex]x = \frac{19}{3} : \frac{4}{3} [/tex]
[tex]x= \frac{19}{3} * \frac{3}{4} [/tex]
⇒ [tex]x = \frac{19}{4} = \frac{16+3}{4} = \frac{16}{4} + \frac{3}{4} =4+ \frac{3}{4} =4 \frac{3}{4} [/tex]
Therefore, Mary needs in total 4 3/4 yards of the fabric.
