Question

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kimani is building shelves for her desk. she has a piece of wood that is 6.5 feet long. after cutting six equal pieces of wood from it, she has 0.8 feet of wood left over.
part a: write an equation that could be used to determine the length of each of the six pieces of wood she 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) (4 points)

Explanation:

Part A

Step1: Define variable

Let \( x \) be the length of each of the six equal pieces.

Step2: Find total length of six pieces

The total length of the six pieces is \( 6x \) (since each piece is \( x \) and there are 6 pieces).

Step3: Set up equation

The original length of the wood is equal to the total length of the six pieces plus the leftover length. So the equation is \( 6x + 0.8 = 6.5 \).

• The left - hand side of the equation \( 6x+0.8 \) represents the total length of the six pieces of wood (which is \( 6x \)) plus the length of the wood that is left over (which is 0.8 feet).
• The right - hand side of the equation, 6.5 feet, represents the original length of the piece of wood.
• According to the problem, the sum of the length of the six cut pieces and the leftover piece should be equal to the original length of the wood. So the equation \( 6x + 0.8=6.5 \) correctly models the relationship between the original length, the length of the cut pieces, and the leftover length.

Step1: Subtract 0.8 from both sides

We start with the equation \( 6x+0.8 = 6.5 \). Subtract 0.8 from both sides to isolate the term with \( x \):
\( 6x+0.8 - 0.8=6.5 - 0.8 \)
Simplifying both sides, we get \( 6x=5.7 \).

Step2: Divide both sides by 6

To solve for \( x \), divide both sides of the equation \( 6x = 5.7 \) by 6:
\( x=\frac{5.7}{6} \)

Step3: Calculate the value of x

\( x = 0.95 \)

Answer:

The equation is \( 6x + 0.8 = 6.5 \) where \( x \) is the length of each of the six pieces.

Part B