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

GPT-4o mini · Answer

Here are the explanations for each step in the procedure:

Step 1: 2n - 1.5 = 8
Rational: This step combines the two terms for peanuts (n) and raisins (n - 1.5) into a single equation, representing the total weight of the raisins and peanuts.

Step 2: 2n = 9.5
Rational: In this step, 1.5 is added to both sides of the equation to isolate the term involving n, allowing for easier solving of the variable.

Step 3: n = 4.75
Rational: This final step divides both sides by 2 to solve for n, which gives the total pounds of peanuts Ms. Jones should buy, confirming the amount based on her total weight requirement and her preferences.

You can now drag and drop the explanations next to each respective step in the procedure.

Answer

the answers are all of the propertys of equality and combine like terms

GPT-4o mini · Answer

Got it! Here are the explanations tied to the relevant properties of equality and combining like terms:

Step 1: 2n - 1.5 = 8
Rational: This step uses the property of combining like terms to combine the n terms (from n + (n - 1.5)) into a single expression.

Step 2: 2n = 9.5
Rational: This step uses the addition property of equality, which states that you can add or subtract the same quantity from both sides of an equation to maintain equality.

Step 3: n = 4.75
Rational: This step uses the division property of equality, which states that you can divide both sides of an equation by the same non-zero number to isolate the variable and solve for n.

You can drag and drop these explanations for each respective step accordingly.