Read the word problem. Look at the student's work and solution. Henry and Rick have 265.3 downloaded minutes of music. If Henry has 112 minutes, how many minutes belong to Rick?

Question

INCORRECT WORK
________________
r = the number of minutes that belong to Rick.
112+r=265.3
-112
+112
r = 377.3
Rick has 377.3 minutes.
___________________

Part A: Identify the error in the student's work and describe it.

Answer 1

The error in the student's work lies in the incorrect arithmetic performed when solving for Rick's minutes.

The correct approach should be to set up the equation correctly and then isolate \( r \):

Starting from the equation: \[ 112 + r = 265.3 \]

To solve for \( r \), you need to subtract 112 from both sides:

\[ r = 265.3 - 112 \]

Instead, the student incorrectly added 112 to both sides of the equation after setting it up. Therefore, they stated:

\[ r = 377.3 \]

This is incorrect because it should have been calculated as follows:

\[ r = 265.3 - 112 = 153.3 \]

So, the correct answer is that Rick has 153.3 minutes of music, not 377.3 minutes. The student's mistake was in performing the wrong operation (addition instead of subtraction) to isolate \( r \).

Answer 2

wrong try again

Answer 3

I apologize for any confusion. Let me clarify the discovered error.

Error Identification:

The critical mistake in the student's work occurs when they attempt to isolate \( r \). The student correctly set up the equation \( 112 + r = 265.3 \) but then incorrectly solved for \( r \).

Instead of correctly subtracting 112 from both sides to isolate \( r \):

1. Correct Step: \( r = 265.3 - 112 \)
2. Student's Incorrect Step: The student calculated \( r \) as \( 112 + r = 265.3 \) and then stated \( r = 377.3 \) due to an incorrect addition, failing to perform the necessary subtraction.

Thus, the error is in the calculation of \( r \). The student misapplied the equation by adding instead of subtracting, leading to the incorrect conclusion that Rick has 377.3 minutes instead of the correct answer, which is:

Rick's minutes: \( r = 265.3 - 112 = 153.3 \).

Thank you for your patience, and I hope this answer correctly highlights the error in the student's work.