Question

Select the correct text.

Regina’s teacher recently gave her a homework assignment on solving equations. Since she has been thinking about saving for a new cell phone, she decided to use the assignment as an opportunity to model a savings plan.

She created this equation to model the situation. In it, y represents the total amount saved for the new cell phone, 74 is the amount of money she has now, 40 is the amount of money she saves each month for the phone, and x represents the number of months since she started saving a regular amount:

74 + 40x = y.

She then solved the equation to determine how many months she’d need to save to have enough to purchase the new cell phone. Review her work, and select the error.

Justification
1: given

2: subtraction property of equality

3: simplification

4: multiplication property of equality

5: simplification

6: substitution, y = 834

7: simplification

Step 1: 74 + 40x = y

Step 2: 74 + 40x − 74 = y − 74

Step 3: 40x = y − 74

Step 4:
=
Step 5: x =
Step 6: x =
Step 7: x = 19

Answer 1

The error in the given steps is Step 4:

Step 4:

This step is missing an operation. It should specify that the right-hand side should be multiplied by 40, just like the left-hand side:

40x = 40(y - 74)

Therefore, the correct step 4 should be:

40x = 40y - 296

The error is that the multiplication of 40 is not applied to both terms on the right-hand side.