Sandy is working with a carpenter to frame a house. They are using 8-foot-long boards, but each board must be cut to be 7 feet [tex]\(10 \frac{3}{4}\)[/tex] inches long. How much is cut off each board?

Note: 1 foot [tex]\(= 12\)[/tex] inches

A. [tex]\(\frac{3}{4}\)[/tex] inch
B. [tex]\(\frac{3}{4}\)[/tex] inches
C. [tex]\(1 \frac{1}{4}\)[/tex] inches
D. 7 inches



Answer :

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