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.

Question

Given n + (n - 1.5) = 8
Step 1: 2n - 1.5 = 8 Rational:
Step 2: 2n = 9.5 Rational:
Step 3: n = 4.75 Rational:
multiplication property of equality
addition property of equality
subtraction property of equality
division property of equality
combine like terms

Answer 1

Here’s how to associate each step with the correct explanation:

Step 1: 2n - 1.5 = 8
Rational: addition property of equality
(You are adding 1.5 to both sides of the equation to eliminate the -1.5 on the left side.)

Step 2: 2n = 9.5
Rational: subtraction property of equality
(You subtract 1.5 from both sides, moving it to the right side of the equation.)

Step 3: n = 4.75
Rational: division property of equality
(You divide both sides by 2 to isolate n.)

So the complete matching is:

• Step 1: 2n - 1.5 = 8 Rational: addition property of equality
• Step 2: 2n = 9.5 Rational: subtraction property of equality
• Step 3: n = 4.75 Rational: division property of equality