Question

150 is 25% of what number? Four students solved this problem using equivalent ratios. Choose the student whose work is correct.
Liam's work. StartFraction part Over whole EndFraction = StartFraction 25 times 6 Over 100 times 6 EndFraction = StartFraction 150 Over 600 EndFraction
Yasmin's work. StartFraction part over whole EndFraction = StartFraction 25 times 6 Over 150 times 6 EndFraction = StartFraction 150 Over 900 EndFraction
Bill's work. StartFraction part Over whole EndFraction = StartFraction 100 divided by 5 Over 25 divided by 5 EndFraction = StartFraction 20 Over 5 EndFraction
Isabella's work. StartFraction part Over whole EndFraction = StartFraction 150 divided by 6 Over 100 divided by 6 EndFraction = StartFraction 25 Over 16.67 EndFraction

Answer 1

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:

1. **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 \( 600 \).

2. **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.

3. **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.

4. **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.