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:

$6.5 - 0.8 = 5.7 \, \text{feet}$

Let $x$ 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 $6x$. Therefore, the equation that represents this situation is:

$6x = 5.7$

Part B: Explanation of the equation

The equation $6x = 5.7$ 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 $x$ by 6 gives the total length of the six pieces.

Part C: Solving the equation

Now, let's solve for $x$.

1. Start with the equation:

$6x = 5.7$

2. To find $x$, divide both sides of the equation by 6:

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

3. Perform the division:

$x = 0.95$

So, the length of each of the six pieces is $0.95$ feet.

Final Answer:

• The equation is $6x = 5.7$.
• The length of each piece is $0.95$ 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.