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:Response area

Answer 1

Sure! Let's break down each step of the equation and provide an explanation for each one.

**Given:** \( n + (n - 1.5) = 8 \)

**Step 1:** \( 2n - 1.5 = 8 \)
**Rationale:** This step combines like terms. The expression \( n + (n - 1.5) \) simplifies to \( 2n - 1.5 \) by adding the \( n \) terms together and subtracting 1.5.

**Step 2:** \( 2n = 9.5 \)
**Rationale:** This step adds 1.5 to both sides of the equation to isolate the term with \( n \) on one side. By performing this operation, the equation becomes \( 2n - 1.5 + 1.5 = 8 + 1.5 \), which simplifies to \( 2n = 9.5 \).

**Step 3:** \( n = 4.75 \)
**Rationale:** This step divides both sides of the equation by 2 to solve for \( n \). To find the value of \( n \), the equation \( 2n = 9.5 \) is divided by 2, resulting in \( n = \frac{9.5}{2} = 4.75 \).

### Summary
- Step 1: Combine like terms.
- Step 2: Isolate the variable term by adding 1.5 to both sides.
- Step 3: Solve for the variable by dividing both sides by 2.