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.

Question

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

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Answer 1

Here is the breakdown and corresponding rationales for each step in the procedure:

Step 1: 2n − 1.5 = 8
Rationale: Combine like terms to isolate the variable 'n' on one side of the equation. The equation starts as n + (n - 1.5) = 8, which simplifies to 2n - 1.5 = 8.

Step 2: 2n = 9.5
Rationale: Add 1.5 to both sides of the equation to eliminate the constant term on the left side. This allows us to solve for 'n' more easily.

Step 3: n = 4.75
Rationale: Divide both sides of the equation by 2 to solve for 'n'. This reveals how many pounds of peanuts Ms. Jones should buy.

You can drag and drop these rationales next to each corresponding step in your procedure.