Question

select the correct answer.
katrina is building a deck. she cuts 3 lengths of wood from a 72-inch board. the first length is $30\frac{3}{4}$ inches. the second length is $12\frac{1}{4}$ inches. and the third length is $16\frac{1}{4}$ inches. how much of the original board remains after katrina makes her cuts?
\\(\bigcirc\\) a. \\(12\frac{1}{4}\\)
\\(\bigcirc\\) b. \\(12\frac{1}{2}\\)
\\(\bigcirc\\) c. \\(12\frac{3}{4}\\)
\\(\bigcirc\\) d. \\(13\frac{3}{4}\\)

Explanation:

Step1: Sum the cut lengths

First, add the integer parts and the fractional parts separately:
Integer sum: $30 + 12 + 16 = 58$
Fractional sum: $\frac{3}{4} + \frac{1}{4} + \frac{1}{4} = \frac{5}{4} = 1\frac{1}{4}$
Total cut length: $58 + 1\frac{1}{4} = 59\frac{1}{4}$

Step2: Subtract from original length

Subtract the total cut length from the 72-inch board:
$72 - 59\frac{1}{4} = 71\frac{4}{4} - 59\frac{1}{4} = 12\frac{3}{4}$

Answer:

C. $12\frac{3}{4}$