13 pieces of board is needed to fit across the front of the gate
Solution:
Given that, A carpenter is building a gate that will be [tex]3\frac{1}{4}[/tex] feet wide
The gate will be made of boards 3 inches wide
From given statement,
Width of gate = [tex]3\frac{1}{4} = \frac{4 \times 3 + 1}{4} = \frac{13}{4} \text{ feet }[/tex]
Width of boards = 3 inches
Let us convert inches to feet
Use the conversion factor
1 feet = 12 inches
Therefore,
[tex]1 \text{ inch } = \frac{1}{12} \text{ feet}[/tex]
[tex]3 \text{ inches } = \frac{1}{12} \times 3 \text{ feet } = \frac{1}{4} \text{ feet }[/tex]
Thus width of board = [tex]\frac{1}{4} \text{ feet }[/tex]
How many pieces of board will it take to fit across the front of the gate?
This can be found by following formula:
[tex]\text{number of boards} = \frac{\text{width of gate}}{\text{ width of board }}[/tex]
Substituting the values we get,
[tex]number\ of\ boards = \frac{\frac{13}{4}}{\frac{1}{4}} = \frac{13}{4} \times \frac{4}{1} = 13[/tex]
Thus 13 pieces of board is needed to fit across the front of the gate
