Certainly! Let's solve the problem step by step.
### Step 1: Determine the Greatest Length of Each Piece
To find the greatest length of each piece that John can cut from the three pieces of wood, we need to find the greatest common divisor (GCD) of the three lengths: 72 inches, 60 inches, and 42 inches.
The greatest length of each piece that we can cut is 6 inches.
### Step 2: Calculate the Number of Pieces for Each Length
Next, we will calculate how many pieces of 6 inches can be cut from each length.
1. For the 72-inch piece:
[tex]\[
\text{Number of pieces} = \frac{72}{6} = 12
\][/tex]
2. For the 60-inch piece:
[tex]\[
\text{Number of pieces} = \frac{60}{6} = 10
\][/tex]
3. For the 42-inch piece:
[tex]\[
\text{Number of pieces} = \frac{42}{6} = 7
\][/tex]
### Step 3: Calculate the Total Number of Pieces
Finally, add the number of pieces from each length to get the total number of pieces.
[tex]\[
\text{Total number of pieces} = 12 + 10 + 7 = 29
\][/tex]
### Summary
- The greatest length of each piece he can cut is 6 inches.
- From the 72-inch piece, he will get 12 pieces.
- From the 60-inch piece, he will get 10 pieces.
- From the 42-inch piece, he will get 7 pieces.
- In total, he will have 29 pieces.
So, John can cut the pieces of wood into a total of 29 pieces, each 6 inches in length.
