Let
x-------> remainder of the original board
we know that
[tex]72=30\frac{3}{4} +12\frac{1}{4}+16\frac{1}{4} +x[/tex] ------> equation [tex]1[/tex]
Convert mixed numbers to an improper fractions
[tex]30\frac{3}{4}=\frac{30*4+3}{4}=\frac{123}{4}[/tex]
[tex]12\frac{1}{4}=\frac{12*4+1}{4}=\frac{49}{4}[/tex]
[tex]16\frac{1}{4}=\frac{16*4+1}{4}=\frac{65}{4}[/tex]
Substitute the values in the equation [tex]1[/tex] and solve for x
[tex]72=\frac{123}{4} +\frac{49}{4}+\frac{65}{4} +x[/tex]
[tex]72=\frac{237}{4} +x[/tex]
solve for x
[tex]x=72-\frac{237}{4}[/tex]
[tex]x=72-59.25[/tex]
[tex]x=12.75\ inches[/tex]
convert to mixed number
[tex]x=12.75\ inches=12+0.75=12+\frac{3}{4}=12\frac{3}{4}\ inches[/tex]
therefore
the answer is
[tex]12\frac{3}{4}\ inches[/tex]
