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.
Part B: Explain how you know the equation from Part A is correct.
Part C: Solve the equation from Part A. Show every step of your work.
Part A:
Let x be the length of each of the five pieces of wood cut from the 4.5 feet long piece of wood. The equation that could be used to determine the length of each piece is:
5x + 0.7 = 4.5
Part B:
We know the equation is correct because it takes into account that Warren cut five pieces of wood that are equal in length from a 4.5 feet long piece of wood. The total length of the five pieces of wood should equal the length of the original piece of wood, minus the leftover wood he has. In other words, 5x represents the total length of the five pieces of wood cut, and 0.7 represents the amount of wood left over after the cutting.
Part C:
5x + 0.7 = 4.5
5x = 4.5 - 0.7
5x = 3.8
x = 3.8/5
x = 0.76
Therefore, each of the five pieces of wood that Warren cut is 0.76 feet long.