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