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:
Let 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 . Therefore, the equation that represents this situation is:
Part B: Explanation of the equation
The equation 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 by 6 gives the total length of the six pieces.
Part C: Solving the equation
Now, let's solve for .
- Start with the equation:
- To find , divide both sides of the equation by 6:
- Perform the division:
So, the length of each of the six pieces is feet.
Final Answer:
- The equation is .
- The length of each piece is feet.
Do you want more details or have any questions?
Here are some related questions for practice:
- If she had 7 feet of wood and left 1.2 feet, what would be the length of each piece?
- What if Kimani cut 8 pieces of wood instead of 6? How would you set up the equation?
- If each piece of wood was 1 foot long, how much wood would she have left?
- How would the equation change if she left 1 foot of wood after cutting?
- 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
-
Suitable Grade Level
Grades 5-7
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