Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.

Question

Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.

Part A: Write an equation that could be used to determine the length of each of the five pieces of wood he cut. (1 point)

Part B: Explain how you know the equation from Part A is correct. (1 point)

Part C: Solve the equation from Part A. Show every step of your work. (2 points)

Answer 1

Part A: Let x be the length of each piece of wood he cut. The equation to determine the length of each piece of wood can be written as:

5x + 0.7 = 4.5

Part B: The equation is correct because it takes into account that Warren cut five equal pieces of wood, and the total length of those five pieces plus the leftover wood should equal the initial length of 4.5 feet.

Part C: To solve the equation, we can follow these steps:

5x + 0.7 = 4.5

Subtract 0.7 from both sides:

5x = 4.5 - 0.7

5x = 3.8

Divide both sides by 5:

x = 3.8 / 5

x = 0.76

Therefore, each piece of wood Warren cut is 0.76 feet long.

Answer 2

Part A: The equation that could be used to determine the length of each of the five pieces of wood Warren cut would be:

5x + 0.7 = 4.5

Where "x" represents the length of each piece of wood.

Part B: We know the equation from Part A is correct because we can break down the problem into two parts: the five pieces of wood that were cut and the leftover wood. The total length of the five pieces of wood must equal the initial length of the wood, minus the length of the leftover wood.

Part C: To solve the equation from Part A and find the length of each piece of wood, we can follow these steps:

1. Subtract 0.7 from both sides of the equation:
5x = 4.5 - 0.7
5x = 3.8

2. Divide both sides of the equation by 5 to isolate "x":
x = 3.8 / 5
x = 0.76

Therefore, the length of each piece of wood Warren cut is 0.76 feet.

Answer 3

Part A: The equation that could be used to determine the length of each of the five pieces of wood Warren cut can be written as:

Length of each cut = (Total length of wood - Leftover length) / Number of cuts

Let's assign variables to the values in the equation:
Let L be the length of each cut.
Let T be the total length of the wood.
Let R be the leftover length of wood.
Let N be the number of cuts.

Using the variables, the equation becomes:
L = (T - R)/N

Part B: We can verify that the equation from Part A is correct by substituting the given values and checking if it holds true. In this case, the given values are:
T = 4.5 feet (total length of wood)
R = 0.7 feet (leftover length of wood)
N = 5 (number of cuts)

Substituting these values into the equation:
L = (4.5 - 0.7)/5
L = 3.8/5
L = 0.76 feet

The equation holds true, and we have found that each piece of wood Warren cut is 0.76 feet long.

Part C: To solve the equation from Part A and find the length of each cut, we substitute the given values into the equation:

L = (T - R)/N
L = (4.5 - 0.7)/5
L = 3.8/5
L = 0.76 feet

Therefore, the length of each of the five pieces of wood Warren cut is 0.76 feet.