Given that BLUE silk used to make one braidsmaid dress = [tex] 4 \frac{1}{8} [/tex] yards
Given that "[tex] 3 \frac{5}{8} [/tex] yards of the same fabric to make another one" which means BLUE silk is used for another dress too.
BLUE silk used to make another dress = [tex] 3 \frac{5}{8} [/tex] yards
Now we have to find how many yards of blue silk used so we will just add both numbers.
[tex] 4 \frac{1}{8} +3 \frac{5}{8}[/tex]
[tex] = 4+3 +\frac{1}{8}+ \frac{5}{8}[/tex]
[tex] = 7 +\frac{6}{8}[/tex]
[tex] = 7 +\frac{3}{4}[/tex]
Hence final answer is [tex] 7 \frac{3}{4}[/tex] yards.