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

Answer 1

Let's break down each step and provide the appropriate rational explanations for what happens in each step of the equation \( n+(n−1.5)=8 \).

Step 1: 2n−1.5=8
Rational: This step combines like terms. The equation \( n + (n - 1.5) \) simplifies to \( 2n - 1.5 \) by adding \( n \) and \( n \) together and then subtracting \( 1.5 \).

Step 2: 2n=9.5
Rational: In this step, you add \( 1.5 \) to both sides of the equation to isolate the term with \( n \). By adding \( 1.5 \) to both sides of \( 2n - 1.5 = 8 \), you obtain \( 2n = 8 + 1.5 \), which simplifies to \( 2n = 9.5 \).

Step 3: n=4.75
Rational: This step involves dividing both sides of the equation by \( 2 \) to solve for \( n \). Since \( 2n = 9.5 \), dividing both sides by \( 2 \) yields \( n = \frac{9.5}{2} = 4.75 \).

In summary:

• Step 1 explanation: Combining like terms.
• Step 2 explanation: Isolating the \( n \) term by adding \( 1.5 \) to both sides.
• Step 3 explanation: Dividing by \( 2 \) to solve for \( n \).

Answer 2

the answer choices are
Multiplication Property Of Equality, Division Property Of Equality, Addition Property Of Equality, Subtraction Property Of Equality, and Combine Like Terms

Answer 3

Thank you for providing the answer choices. Here’s how each step corresponds to those options:

Step 1: 2n−1.5=8
Rational: Combine Like Terms
This step simplifies the left side of the equation by combining the like terms \( n + (n - 1.5) \).

Step 2: 2n=9.5
Rational: Addition Property Of Equality
In this step, \( 1.5 \) is added to both sides of the equation \( 2n - 1.5 = 8 \) to isolate the term with \( n \).

Step 3: n=4.75
Rational: Division Property Of Equality
Here, both sides of the equation \( 2n = 9.5 \) are divided by \( 2 \) to solve for \( n \).

So, to summarize for each step:

• Step 1: Combine Like Terms
• Step 2: Addition Property Of Equality
• Step 3: Division Property Of Equality