six office desks that are $3\frac{1}{12}$ feet long are to be placed together on a wall that is…

six office desks that are $3\frac{1}{12}$ feet long are to be placed together on a wall that is $18\frac{7}{12}$ feet long. will they fit on the wall? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. yes, if no more than a total of foot is needed for spacing between desks. (type an integer or a simplified fraction.) b. no, they do not all fit along the wall.

six office desks that are $3\frac{1}{12}$ feet long are to be placed together on a wall that is $18\frac{7}{12}$ feet long. will they fit on the wall? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. yes, if no more than a total of foot is needed for spacing between desks. (type an integer or a simplified fraction.) b. no, they do not all fit along the wall.

Answer

Explanation:

Step1: Calculate total length of desks

The length of one desk is $3\frac{1}{12}=\frac{3\times12 + 1}{12}=\frac{37}{12}$ feet. For 6 desks, the total length is $6\times\frac{37}{12}=\frac{37}{2}=18.5$ feet.

Step2: Convert wall - length to decimal

The length of the wall is $18\frac{7}{12}=\frac{18\times12+7}{12}=\frac{216 + 7}{12}=\frac{223}{12}\approx18.583$ feet.

Step3: Find available space for spacing

The available space for spacing is $\frac{223}{12}-\frac{37}{2}=\frac{223}{12}-\frac{222}{12}=\frac{1}{12}$ feet.

Answer:

A. Yes, if no more than a total of $\frac{1}{12}$ foot is needed for spacing between desks.