Question

Ms. Jones is buying raisins and peanuts. She needs 8 pounds total, and she wants to have 1.5 more pounds of peanuts than raisins. The solution to the equation below shows how she can determine the solution for n, the number of pounds of peanuts she should buy. What explanations can be made for each of the three steps in the procedure? Drag and drop the correct explanation next to each step. Given: n+(n−1.5)=8 Step 1: 2n−1.5=8 Rational:Response area Step 2: 2n=9.5 Rational:Response area Step 3: n=4.75 Rational:s

Answer 1

Let's break down the equation and the steps involved, along with the rational explanations for each step.

Given the equation:
\[ n + (n - 1.5) = 8 \]

**Step 1: 2n - 1.5 = 8**
- **Rational:** This step combines the terms \( n + (n - 1.5) \) into a single equation by adding the two \( n \) terms together and then simplifying the equation. The expression \( n + n = 2n \) and the constant term \(-1.5\) remains, leading to \( 2n - 1.5 = 8 \).

**Step 2: 2n = 9.5**
- **Rational:** In this step, we isolate \( 2n \) by adding \( 1.5 \) to both sides of the equation. This leads to \( 2n - 1.5 + 1.5 = 8 + 1.5 \), which simplifies to \( 2n = 9.5 \).

**Step 3: n = 4.75**
- **Rational:** Here, we solve for \( n \) by dividing both sides of the equation by \( 2 \). This means \( n = \frac{9.5}{2} \), which simplifies to \( n = 4.75 \).

So the full explanations for each step are as follows:

1. **Step 1:** 2n - 1.5 = 8 **Rational:** Combines terms to simplify the equation.
2. **Step 2:** 2n = 9.5 **Rational:** Isolates \( 2n \) by adding \( 1.5 \) to both sides.
3. **Step 3:** n = 4.75 **Rational:** Solves for \( n \) by dividing by \( 2 \).