Math Problem Statement

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)

Solution

Let's break down the problem step by step.

Part A: Writing the equation

Kimani has a total of 6.5 feet of wood, and after cutting six equal pieces, she has 0.8 feet of wood left over. This means the length of all six pieces combined is:

6.50.8=5.7feet6.5 - 0.8 = 5.7 \, \text{feet}

Let xx represent the length of each of the six pieces. Since the six pieces are equal in length, the total length of all six pieces is 6x6x. Therefore, the equation that represents this situation is:

6x=5.76x = 5.7

Part B: Explanation of the equation

The equation 6x=5.76x = 5.7 is correct because:

  • The total length of the six pieces of wood equals 5.7 feet (the amount of wood left after subtracting the 0.8 feet of leftover wood from the 6.5 feet).
  • Each of the six pieces is the same length, so multiplying the unknown length xx by 6 gives the total length of the six pieces.

Part C: Solving the equation

Now, let's solve for xx.

  1. Start with the equation:

6x=5.76x = 5.7

  1. To find xx, divide both sides of the equation by 6:

x=5.76x = \frac{5.7}{6}

  1. Perform the division:

x=0.95x = 0.95

So, the length of each of the six pieces is 0.950.95 feet.

Final Answer:

  • The equation is 6x=5.76x = 5.7.
  • The length of each piece is 0.950.95 feet.

Do you want more details or have any questions?
Here are some related questions for practice:

  1. If she had 7 feet of wood and left 1.2 feet, what would be the length of each piece?
  2. What if Kimani cut 8 pieces of wood instead of 6? How would you set up the equation?
  3. If each piece of wood was 1 foot long, how much wood would she have left?
  4. How would the equation change if she left 1 foot of wood after cutting?
  5. What if she used the leftover wood for another project? How much would be left?

Tip: When cutting equal parts, always subtract any leftovers before dividing.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Total length of wood after cutting = Total length - Leftover wood
6x = 5.7

Theorems

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Suitable Grade Level

Grades 5-7