Question

Mrs. Robinson wrote an equation on the board. She asked the students to solve for the variable, k. Jeff solved it on his paper using the following steps.

Step 1 k over 0.12 equals 2.4
Step 2 the product of 0.12 and k over 0.12 equals 2.4 times 2.4
Step 3 k = 5.76


Part A: Review Jeff's work for solving the equation. State the step in which the error occurred, and describe the error using your mathematics vocabulary. (8 points)

Part B: Solve the equation, correcting any errors you may find. Show all the steps in your work. (4 points)

Answer 1

Step-by-step explanation:

AI-generated answer

Part A: The error in Marcus' work occurred in Step 2. The error is that he incorrectly stated that the sum of 0.14 and w over 0.14 equals 4.2 plus 0.14. This statement is incorrect.

The correct statement should be: w over 0.14 plus 1 equals 4.2 plus 0.14. This is because when you divide w by 0.14, you get w over 0.14. Adding 1 to both sides of the equation allows you to isolate the variable on one side.

Part B: Let's correct the error and solve the equation step by step:

Step 1: w over 0.14 equals 4.2

To isolate w, we need to multiply both sides of the equation by 0.14:

w = 4.2 * 0.14

Step 2: w = 0.588

So the corrected value for w is 0.588.

Answer 2

Jeff made an error in Step 2 by multiplying instead of dividing. The corrected solution is k = 0.288.

Step-by-step explanation:

Part A:
Jeff made an error in Step 2 of his solution. The error occurred when he multiplied both sides of the equation by 2.4. The correct step should have been to divide both sides by 0.12, not multiply.

Part B:
To solve the equation correctly, we need to correct the error made by Jeff in Step 2. Here are the correct steps:

Step 1: k/0.12 = 2.4 (given)
Step 2: (k/0.12) * 0.12 = 2.4 * 0.12
Step 3: k = 0.288