To determine which student solved the equation [tex]\(\frac{w}{13.5}=9.7\)[/tex] correctly, let’s analyze the work of each student in detail.
### Kwan's Work:
1. Kwan starts with the equation: [tex]\(\frac{w}{13.5} = 9.7\)[/tex].
2. To isolate [tex]\( w \)[/tex], multiply both sides of the equation by 13.5:
[tex]\[
w = 9.7 \times 13.5
\][/tex]
3. Calculate the product:
[tex]\[
9.7 \times 13.5 = 130.95
\][/tex]
4. Therefore, Kwan concludes:
[tex]\[
w = 130.95
\][/tex]
### Amala's Work:
1. Amala starts with the equation: [tex]\(\frac{w}{13.5} = 9.7\)[/tex].
2. She performs the operation [tex]\(13.5 - 9.7\)[/tex]:
[tex]\[
13.5 - 9.7 = 3.8
\][/tex]
3. Amala concludes with the result [tex]\( 3.8 \)[/tex].
### Sid's Work:
1. Sid starts with the equation: [tex]\(\frac{w}{13.5} = 9.7\)[/tex].
2. He performs the operation [tex]\(13.5 + 9.7\)[/tex]:
[tex]\[
13.5 + 9.7 = 23.2
\][/tex]
3. Sid concludes with the result [tex]\( 23.2 \)[/tex].
### Correct Solution Analysis:
To solve the equation [tex]\(\frac{w}{13.5} = 9.7\)[/tex] correctly, you need to isolate [tex]\( w \)[/tex] by multiplying both sides by 13.5. This results in:
[tex]\[
w = 9.7 \times 13.5 = 130.95
\][/tex]
From this, it is clear that Kwan used the correct method to solve the equation and arrived at the correct result. Neither Amala nor Sid performed the correct operations needed to solve for [tex]\( w \)[/tex].
### Conclusion:
The student who solved the equation [tex]\(\frac{w}{13.5} = 9.7\)[/tex] correctly is Kwan.
