Question

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)

Answer 1

**Part A: Equation**

Let L represent the length of each piece of wood Kimani cut. She started with a 6.5 feet long piece and cut six equal pieces from it. Afterward, she had 0.8 feet left. So, we can write the equation as:

```css

6.5 - 6L = 0.8

```

**Part B: Explanation**

We know this equation is correct because it accurately models the situation. Kimani began with a piece of wood 6.5 feet long, cut six equal pieces, and was left with 0.8 feet. The equation represents this situation by subtracting the total length of the six pieces (6L) from the initial length (6.5 feet) and ensuring that it equals the remaining wood (0.8 feet).

**Part C: Solution**

Now, let's solve the equation for L:

```css

6.5 - 6L = 0.8

```

First, subtract 6.5 from both sides to isolate -6L on the left side:

```css

-6L = 0.8 - 6.5

```

```css

-6L = -5.7

```

To find L, divide both sides by -6:

```css

L = -5.7 / -6

```

```css

L = 0.95

```

So, each piece of wood that Kimani cut is approximately 0.95 feet long.

Answer 2

A: Equation: 6x + 0.8 = 6.5

C: 0.95 feet

Explanation:

Part A:

Let x be the length of each of the six pieces of wood she cut. The equation is:

6x + 0.8 = 6.5

This equation represents the total length of the wood (6.5 feet) minus the leftover wood (0.8 feet) is equal to the sum of the lengths of the six pieces of wood (6x).

Part B:

We know the equation is correct because it satisfies the following conditions:

• The total length of the wood (6.5 feet) minus the leftover wood (0.8 feet) is equal to the sum of the lengths of the six pieces of wood (6x).
• The length of each piece of wood (x) is a positive number.

Part C:

To solve the equation, we can subtract 0.8 from both sides:

6x + 0.8 - 0.8 = 6.5 - 0.8

6x = 5.7

To find the value of x, we can divide both sides by 6:

`\sf (6x )/(6) =( 5.7 )/(6)`

x = 0.95

Therefore, each piece of wood is 0.95 feet long.