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.
-
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 \(600\).
-
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 \(16.67%\)).
-
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.
-
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.
1 answer