Mrs. Jones wrote an equation on the board. She asked the students to solve for the variable, w. Marcus solved it on his paper using the following steps.
Step 1 w over 0.14 equals 4.2
Step 2 the sum of 0.14 and w over 0.14 equals 4.2 plus 0.14
Step 3 w = 4.34
Part A: Review Marcus' 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)
Part A: The error occurred in Step 2. Marcus incorrectly added the two fractions instead of multiplying them.
Part B:
Step 1: w over 0.14 = 4.2
Step 2: Multiply both sides by 0.14: 0.14w = 4.2 * 0.14
Step 3: Subtract 0.14 from both sides: 0.14w - 0.14 = 4.2 * 0.14 - 0.14
Step 4: Simplify: 0.14w = 4.06
Step 5: Divide both sides by 0.14: w = 4.06 / 0.14
Step 6: Simplify: w = 29
30
did the test
Part A: The error in Marcus' work occurred in Step 2. The error is that Marcus mistakenly added 0.14 to both sides of the equation instead of subtracting it.
Part B: To solve the equation correctly, let's go through the steps:
Step 1: w/0.14 = 4.2
Step 2: Multiply both sides of the equation by 0.14 to get rid of the fraction on the left side:
(0.14)(w/0.14) = (0.14)(4.2)
This simplifies to:
w = 0.588
So the correct solution for the equation is w = 0.588.
Part A:
Looking at Marcus' work, the error occurred in Step 2. The error can be described as an incorrect application of the addition property of equality. Marcus incorrectly added 0.14 and w/0.14 on both sides of the equation, resulting in an incorrect equation.
Part B:
To solve the equation correctly, we need to isolate the variable, w. Let's go through the steps:
Step 1: w/0.14 = 4.2
To get rid of the fraction, we need to multiply both sides of the equation by 0.14:
0.14 * (w/0.14) = 0.14 * 4.2
w = 0.588
Therefore, the correct solution for the equation is w = 0.588.