Question
Eva spent $12.48 downloading songs, and each song cost $1.29. Four students wrote and solved equations to find x, the number of songs that she downloaded. Which student wrote and solved the equation correctly?
(1 point)
Responses
Megan's Work
x1.29=12.48
x=16
Megan's Work x over 1 point 2 9 is equal to 12 point 4 8 x is equal to 16
Josh's Work
1.29x=12.48
x=10
Josh's Work 1 point 2 9 x is equal to 12 point 4 8 x is equal to 10
Anna's Work
x1.29=12.48
x=13.77
Anna's Work x over 1 point 2 9 is equal to 12 point 4 8 x is equal to 13 point 7 7
Mary's Work
1.29x=12.48
x=9
(1 point)
Responses
Megan's Work
x1.29=12.48
x=16
Megan's Work x over 1 point 2 9 is equal to 12 point 4 8 x is equal to 16
Josh's Work
1.29x=12.48
x=10
Josh's Work 1 point 2 9 x is equal to 12 point 4 8 x is equal to 10
Anna's Work
x1.29=12.48
x=13.77
Anna's Work x over 1 point 2 9 is equal to 12 point 4 8 x is equal to 13 point 7 7
Mary's Work
1.29x=12.48
x=9
Answers
Answered by
GPT-4o mini
To find the number of songs that Eva downloaded, we can set up the equation based on the information provided.
The equation to represent the situation is:
\[
1.29x = 12.48
\]
where \( x \) is the number of songs downloaded.
Now, we'll solve for \( x \):
\[
x = \frac{12.48}{1.29} \approx 9.69
\]
When we calculate:
\[
x = 12.48 \div 1.29 \approx 9.69
\]
That means the equation needs to divide `12.48` by `1.29` to find \( x \), and it's incorrect to state that \( x \) would yield a whole number since songs must be whole number values.
However, if we check each student's work, we identify errors in their calculations related to how they handled the equation:
1. **Megan**:
- She wrote \( x \cdot 1.29 = 12.48 \) and claimed \( x = 16 \), which is incorrect.
2. **Josh**:
- He wrote \( 1.29x = 12.48 \) and claimed \( x = 10 \), which is also incorrect as \( 12.48 \div 1.29 \) does not equal 10.
3. **Anna**:
- She wrote \( x \cdot 1.29 = 12.48 \) and claimed \( x = 13.77 \), which is incorrect.
4. **Mary**:
- She wrote \( 1.29x = 12.48 \) and claimed \( x = 9 \). However, \( 12.48 \div 1.29 \) is approximately \( 9.69 \), so while her setup was correct, her calculation is incorrect.
There seems to be some confusion because none of them presented the correct answer, but the only equations that set up correctly are from **Josh and Mary**, even though neither of them calculated the final answer correctly.
If we conclude from their expressions:
- Megan and Anna wrote the wrong equations.
- Josh and Mary used the correct format but both had incorrect answers.
None of the students provided the correct answer, but **Josh and Mary** at least started correctly.
The equation to represent the situation is:
\[
1.29x = 12.48
\]
where \( x \) is the number of songs downloaded.
Now, we'll solve for \( x \):
\[
x = \frac{12.48}{1.29} \approx 9.69
\]
When we calculate:
\[
x = 12.48 \div 1.29 \approx 9.69
\]
That means the equation needs to divide `12.48` by `1.29` to find \( x \), and it's incorrect to state that \( x \) would yield a whole number since songs must be whole number values.
However, if we check each student's work, we identify errors in their calculations related to how they handled the equation:
1. **Megan**:
- She wrote \( x \cdot 1.29 = 12.48 \) and claimed \( x = 16 \), which is incorrect.
2. **Josh**:
- He wrote \( 1.29x = 12.48 \) and claimed \( x = 10 \), which is also incorrect as \( 12.48 \div 1.29 \) does not equal 10.
3. **Anna**:
- She wrote \( x \cdot 1.29 = 12.48 \) and claimed \( x = 13.77 \), which is incorrect.
4. **Mary**:
- She wrote \( 1.29x = 12.48 \) and claimed \( x = 9 \). However, \( 12.48 \div 1.29 \) is approximately \( 9.69 \), so while her setup was correct, her calculation is incorrect.
There seems to be some confusion because none of them presented the correct answer, but the only equations that set up correctly are from **Josh and Mary**, even though neither of them calculated the final answer correctly.
If we conclude from their expressions:
- Megan and Anna wrote the wrong equations.
- Josh and Mary used the correct format but both had incorrect answers.
None of the students provided the correct answer, but **Josh and Mary** at least started correctly.