To determine how much of each 8-foot-long board needs to be cut off to achieve a length of 7 feet [tex]\(10 \frac{3}{4}\)[/tex] inches, follow these steps:
1. Convert the Length of the Board and Required Length to Inches:
- 1 foot is equal to 12 inches. So, an 8-foot-long board is:
[tex]\[
8 \text{ feet} \times 12 \text{ inches/foot} = 96 \text{ inches}
\][/tex]
- To find the length needed for the board, convert 7 feet [tex]\(10 \frac{3}{4}\)[/tex] inches entirely into inches:
[tex]\[
7 \text{ feet} \times 12 \text{ inches/foot} = 84 \text{ inches}
\][/tex]
[tex]\[
10 \text{ inches} + \frac{3}{4} \text{ inch} = 10.75 \text{ inches}
\][/tex]
Therefore, the total required length in inches is:
[tex]\[
84 \text{ inches} + 10.75 \text{ inches} = 94.75 \text{ inches}
\][/tex]
2. Calculate How Much Needs to Be Cut Off:
- Subtract the required length from the original board length:
[tex]\[
96 \text{ inches} - 94.75 \text{ inches} = 1.25 \text{ inches}
\][/tex]
Therefore, the amount cut off each board is [tex]\(1 \frac{1}{4}\)[/tex] inches.
Thus, the answer is:
[tex]\[ \boxed{1 \frac{1}{4} \text{ inches}} \][/tex]
This means the correct choice is:
C. [tex]\(1 \frac{1}{4}\)[/tex] inches
