To determine which student's work is correct, we need to understand the original problem: "150 is 25% of what number?"
We can set up the equation based on the information given:
Let \( x \) be the number we are trying to find. The equation based on the problem is:
\[ 150 = 0.25 \cdot x \]
To find \( x \), we can rearrange the equation:
\[ x = \frac{150}{0.25} \]
Calculating this gives:
\[ x = 150 \div 0.25 = 150 \times 4 = 600 \]
So, \( 150 \) is \( 25% \) of \( 600 \).
Now let's analyze the work done by each student:
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Liam's work: \[ \frac{\text{part}}{\text{whole}} = \frac{25 \times 6}{100 \times 6} = \frac{150}{600} \] This is correct, as \( 150 \) is indeed \( 25% \) of \( 600 \).
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Yasmin's work: \[ \frac{\text{part}}{\text{whole}} = \frac{25 \times 6}{150 \times 6} = \frac{150}{900} \] This is not correct because she claims \( 150 \) is \( 25% \) of \( 900 \) which is not true.
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Bill's work: \[ \frac{100 \div 5}{25 \div 5} = \frac{20}{5} \] This does not relate to the original problem correctly, so it's not valid.
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Isabella's work: \[ \frac{150 \div 6}{100 \div 6} = \frac{25}{16.67} \] This does not represent the problem correctly, as it deviates from the calculations needed.
Conclusion: The correct student is Liam, as his work accurately represents that 150 is 25% of 600.
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