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

1 answer

Let's explain each step of the equation and what occurs in each transformation:

Step 1: \(2n - 1.5 = 8\)

Rational:

This step combines the terms on the left side of the equation. We start with \(n + (n - 1.5) = 8\), which involves adding \(n\) (the weight of raisins) and \((n - 1.5)\) (the weight of peanuts). By combining these like terms, we get \(2n - 1.5 = 8\).

Step 2: \(2n = 9.5\)

Rational:

This step involves isolating the term containing \(n\). To do this, we add 1.5 to both sides of the equation from Step 1. This helps to eliminate the constant on the left side and makes it easier to solve for \(n\). The equation simplifies to \(2n = 9.5\).

Step 3: \(n = 4.75\)

Rational:

In this step, we solve for \(n\) by dividing both sides of the equation \(2n = 9.5\) by 2. This yields \(n = 4.75\), which represents the number of pounds of peanuts that Ms. Jones should buy.

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