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
Explanation:Currently contains Combine Like Terms.

Step 2: 2n=9.5
Explanation:Currently contains Multiplication Property of Equality.

Step 3: n=4.75
Explanation:Currently contains Addition Property of Equality.

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Answer 1

Match each step with the reason:

- Step 1: 2n − 1.5 = 8 — Combine Like Terms (n + n = 2n).
- Step 2: 2n = 9.5 — Addition Property of Equality (added 1.5 to both sides).
- Step 3: n = 4.75 — Multiplication Property of Equality (equivalently, divide both sides by 2 or multiply by 1/2).

Check: 4.75 + (4.75 − 1.5) = 4.75 + 3.25 = 8, so n = 4.75 is correct.