Three pieces of wood are needed for project. They are to be cut from a 90cm long piece of wood. The longest piece is to be 3 times as long as the middle sized piece and the shortest piece is to be 10 cm shorter than the middle sized piece. Can this be done with 2 cuts? If so, tell how.

x-10 + x + 3x=90

x=20 cm, short= 10 cm, longest=60cm

A woodworking project requires three pieces of wood. The longest piece must be 3 times as long as the middle sized piece and the shortest piece must be 6 inches shorter than the middle sized piece. If the three pieces are cut from a single board that is 84 inches long, how long will the shortest piece be?

Yes, this can be done with 2 cuts. Here's how:

1. First, we need to determine the length of the middle-sized piece. Let's assume the middle-sized piece is x cm long.
2. According to the given information, the longest piece is 3 times as long as the middle-sized piece. So, the longest piece would be 3x cm long.
3. The shortest piece is 10 cm shorter than the middle-sized piece. Therefore, the shortest piece would be (x - 10) cm long.
4. To cut the wood into the required pieces with 2 cuts, we can follow these steps:
a. Make the first cut at a distance of x cm from one end of the 90 cm long piece of wood. This will separate the piece into two sections.
b. Make the second cut at a distance of (3x - 10) cm from the first cut. This will separate the longer section into two pieces, one that is 3x cm long and the other that is (x - 10) cm long.

With these two cuts, we will have the three required pieces of wood.

To determine if three pieces of wood can be cut from a 90cm long piece using only 2 cuts, we first need to analyze the relationships given.

Let's assume the middle-sized piece is x cm long.

According to the information provided, the longest piece is 3 times as long as the middle-sized piece:

Longest piece = 3x cm

The shortest piece is 10 cm shorter than the middle-sized piece:

Shortest piece = x - 10 cm

To find out if this can be done with 2 cuts, we need to consider the minimum and maximum lengths of each piece.

Minimum lengths of pieces (if the longest piece is cut first):
- Longest piece = 3x cm
- Middle-sized piece = x cm
- Shortest piece = 0 cm (not possible)

Maximum lengths of pieces (if the shortest piece is cut first):
- Longest piece = 90 cm (if the first cut is made 10 cm from the end, and the second cut is made 80 cm from the other end)
- Middle-sized piece = 80 cm (in order to create a piece 10 cm shorter for the shortest piece)
- Shortest piece = 70 cm

Since the shortest piece can be a minimum of 0 cm and a maximum of 70 cm, which is within the range of possible lengths, it is indeed possible to obtain three pieces of wood with two cuts from a 90 cm long piece.

To achieve this, follow these steps:
1. Make the first cut 10 cm from one end of the 90cm piece of wood.
2. Make the second cut 80 cm from the other end of the wood piece.

By doing this, you will obtain three pieces of wood measuring 70 cm, 80 cm, and 3*80 = 240 cm in length.