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
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which student's work is correct, we can first set up the problem using the equation for percentages. The equation states:
\[
\text{part} = \text{percent} \times \text{whole}
\]
In this case, we know that 150 is 25% of some number (let's call it \( x \)). The equation can be set up as follows:
\[
150 = 0.25 \times x
\]
To solve for \( x \):
\[
x = \frac{150}{0.25} = 150 \times 4 = 600
\]
Now we will evaluate each student's work based on equivalent ratios.
1. **Liam's work:**
\[
\frac{\text{part}}{\text{whole}} = \frac{25 \times 6}{100 \times 6} = \frac{150}{600}
\]
- This is correct since \(150\) 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 incorrect; \(150\) is not \(25\%\) of \(900\) (it is actually \(16.67\%\)).
3. **Bill's work:**
\[
\frac{100 \div 5}{25 \div 5} = \frac{20}{5}
\]
- This does not relate to the question correctly and doesn't provide a valid ratio to solve for the whole number.
4. **Isabella's work:**
\[
\frac{150 \div 6}{100 \div 6} = \frac{25}{16.67}
\]
- This does not correctly set up the ratio needed to solve for \(x\) accurately.
Given this evaluation, **Liam's work** is the correct one, as it correctly demonstrates the relationship between part, whole, and percentage.
\[
\text{part} = \text{percent} \times \text{whole}
\]
In this case, we know that 150 is 25% of some number (let's call it \( x \)). The equation can be set up as follows:
\[
150 = 0.25 \times x
\]
To solve for \( x \):
\[
x = \frac{150}{0.25} = 150 \times 4 = 600
\]
Now we will evaluate each student's work based on equivalent ratios.
1. **Liam's work:**
\[
\frac{\text{part}}{\text{whole}} = \frac{25 \times 6}{100 \times 6} = \frac{150}{600}
\]
- This is correct since \(150\) 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 incorrect; \(150\) is not \(25\%\) of \(900\) (it is actually \(16.67\%\)).
3. **Bill's work:**
\[
\frac{100 \div 5}{25 \div 5} = \frac{20}{5}
\]
- This does not relate to the question correctly and doesn't provide a valid ratio to solve for the whole number.
4. **Isabella's work:**
\[
\frac{150 \div 6}{100 \div 6} = \frac{25}{16.67}
\]
- This does not correctly set up the ratio needed to solve for \(x\) accurately.
Given this evaluation, **Liam's work** is the correct one, as it correctly demonstrates the relationship between part, whole, and percentage.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.