Question

A carpenter is building a gate that will be 3-1/4 feet wide. The gate will be made of boards 3 inches wide. How many pieces of board will it take to fit across the front of the gate?

Answer 1

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 $3\frac{1}{4}$ feet wide

The gate will be made of boards 3 inches wide

From given statement,

Width of gate = $3\frac{1}{4} = \frac{4 \times 3 + 1}{4} = \frac{13}{4} \text{ feet }$

Width of boards = 3 inches

Let us convert inches to feet

Use the conversion factor

1 feet = 12 inches

Therefore,

$1 \text{ inch } = \frac{1}{12} \text{ feet}$

$3 \text{ inches } = \frac{1}{12} \times 3 \text{ feet } = \frac{1}{4} \text{ feet }$

Thus width of board = $\frac{1}{4} \text{ feet }$

How many pieces of board will it take to fit across the front of the gate?

This can be found by following formula:

$\text{number of boards} = \frac{\text{width of gate}}{\text{ width of board }}$

Substituting the values we get,

$number\ of\ boards = \frac{\frac{13}{4}}{\frac{1}{4}} = \frac{13}{4} \times \frac{4}{1} = 13$

Thus 13 pieces of board is needed to fit across the front of the gate