https://file.aiquickdraw.com/mathbot/file/1726622152675j6u9a61s.jpg

Let's analyze and solve the problem.

### Translation of the problem (from French to English):

**"If 24 pieces shown below are to be cut from a rod of 35 3/16 inches in length, what length will remain of the rod? (Allow 1/16" per cut)."**

The key data are:
- Length of the rod: 35 3/16 inches.
- Number of pieces: 24.
- Each cut requires an additional 1/16" of material (lost per cut).

### Steps for the solution:

1. **Determine the length of each piece**: From the diagram, we see that each piece is **5 5/64 inches** long.

2. **Calculate total material used**: The total length of 24 pieces, without considering cuts, is:
   \[
   \text{Total length} = 24 \times 5 \frac{5}{64} \, \text{inches}
   \]

3. **Account for material lost to cuts**: There will be 23 cuts between the 24 pieces, and each cut loses 1/16 inch, so the total material lost to cuts is:
   \[
   \text{Material lost to cuts} = 23 \times \frac{1}{16} \, \text{inches}
   \]

4. **Subtract from the initial rod length**: The remaining length will be the original length of the rod minus the total material used and the material lost to cuts.

Let’s calculate this now.The calculated result shows a negative value (-88.125 inches), which indicates that the total length of the 24 pieces (plus the material lost to cuts) exceeds the length of the rod. This means that it is **not possible** to cut 24 pieces of 5 5/64 inches each from a rod of 35 3/16 inches, while also accounting for 1/16 inch lost per cut.

Would you like a more detailed breakdown or to adjust the parameters? Here are 5 related questions you might consider:

1. What if the length of each piece were reduced to fit within the available rod length?
2. How many pieces can actually be cut from this rod without exceeding its length?
3. How does the amount of material lost to cuts impact the total number of pieces?
4. What would the remaining length be if fewer pieces were cut?
5. Could different cutting techniques reduce the material loss per cut?

**Tip:** Always check if the total material needed exceeds the available stock length before cutting!

Si 24 pièces montrées ci-dessous doivent être coupées à partir d’une tige de 35 3/16” de longueur, quelle longueur restera-t-il de la tige? (permettre 1/16" par coupe).

Learn how to calculate the remaining length of a rod after cutting 24 pieces of specific length, including allowances for material lost in each cut. This problem involves measuring, multiplying fractions, and subtracting to find the final result.

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