Question

how many boards are needed to build a fence that is 150 inches long? show your reasoning.

Explanation:

To solve this, we need to know the length of each board. Since it's not provided, let's assume a common board length (e.g., 6 inches, 10 inches, 12 inches, etc.). Let's assume each board is 10 inches long (you can replace this with the actual board length if given).

Step 1: Define the length of one board

Let’s assume each board is \( l = 10 \) inches long (replace with actual length if known).

Step 2: Calculate the number of boards

The number of boards \( n \) is the total length of the fence divided by the length of one board. So, \( n=\frac{\text{Total Length}}{\text{Length of one board}} \)
Substituting the values: \( n = \frac{150}{10}=15 \)

If the board length is different, say \( l = 6 \) inches:

Step 1: Define the length of one board

\( l = 6 \) inches

Step 2: Calculate the number of boards

\( n=\frac{150}{6} = 25 \)

Since the problem doesn't specify the board length, we need that information. But if we assume a typical board length (e.g., 10 inches as above), the number of boards would be 15 (or adjust based on actual board length).

Answer:

To determine the number of boards, we need the length of one board (\( l \)). The formula is \( \text{Number of Boards} = \frac{150}{l} \). For example, if \( l = 10 \) inches, the number of boards is \( \boldsymbol{15} \); if \( l = 6 \) inches, it is \( \boldsymbol{25} \) (replace with the actual board length to get the exact answer).