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?
Tell the correct explanation next to each step.
Given: n + (n - 1.5) = 8
Step 1: 2n - 1.5 = 8 Rational: BLANK
Step 2: 2n = 9.5 Rational: BLANK
Step 3: n = 4.75 Rational: BLANK

What properties go in the BLANK's? Combine Like Terms, Addition Property of Equality, Division Property of Equality, Multiplication Property of Equality, Subtraction Property of Equality.

Answer 1

Let's fill in the blanks for each step with the correct explanations.

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

Step 1: \( 2n - 1.5 = 8 \)
Rational: Combine Like Terms
(Here, we combine \( n \) and \( n \) to get \( 2n \), and we rewrite \( -1.5 \) properly in the equation.)

Step 2: \( 2n = 9.5 \)
Rational: Addition Property of Equality
(We add \( 1.5 \) to both sides of the equation to isolate the term containing \( n \).)

Step 3: \( n = 4.75 \)
Rational: Division Property of Equality
(We divide both sides by 2 to solve for \( n \).)

So, the completed explanations are:

1. Step 1: Combine Like Terms
2. Step 2: Addition Property of Equality
3. Step 3: Division Property of Equality