Answer:
The fabric left over will be [tex]2\frac{5}{6}[/tex]
Step-by-step explanation:
Total fabric bought= [tex]8\frac{3}{4} \ yd[/tex]
Fabric used for skirt = [tex]1\frac{7}{8} \ yd[/tex]
Fabric used for pants = [tex]2\frac{3}{8} \ yd[/tex]
Fabric used for vest = [tex]1\frac{2}{3} \ yd[/tex]
Total fabric used = Fabric used for skirt+Fabric used for pants+Fabric used for vest
Total fabric used=[tex]1\frac{7}{8}+2\frac{3}{8}+1\frac{2}{3}[/tex]
[tex]=\frac{15}{8}+\frac{19}{8}+\frac{5}{3}\\=\frac{15*3+19*3+5*8}{24}\\=\frac{45+57+40}{24}\\=\frac{142}{24} \\=\frac{71}{12}[/tex]
So, Total fabric used = [tex]\frac{71}{12}[/tex]
Total Fabric left= Total fabric bought-Total fabric used
Total Fabric left=[tex]8\frac{3}{4}-\frac{71}{12}[/tex]
[tex]=\frac{35}{4}-\frac{71}{12}\\=\frac{35*3-71}{12} \\=\frac{105-71}{12}\\=\frac{34}{12}\\=\frac{17}{6}\\=2\frac{5}{6}[/tex]
So, the fabric left over will be [tex]2\frac{5}{6}[/tex]
