Question

which equation below can be used to solve the percent problem using the proportion method, \30 is 50% of what number?\
50 (m) = 30
50/30 = m/100
50/100 = 30/m
30 x 0.050 = m
question 11 (2.5 points)
700 is what percent of 50? use the proportion method.
14%
70%
1400%
1.4%

Explanation:

First Question (Which equation...):

Step1: Recall proportion method for percent

The proportion method for percent problems is $\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}$. For "30 is 50% of what number (let the number be \( m \))", the part is 30, the percent is 50, and the whole is \( m \). So the proportion is $\frac{50}{100}=\frac{30}{m}$.

Step2: Analyze other options

• Option \( 50(m)=30 \): Incorrect, doesn't follow proportion method.
• Option \( \frac{50}{30}=\frac{m}{100} \): Swaps part and percent, incorrect.
• Option \( 30\times0.050 = m \): Uses decimal method, not proportion, and 50% is 0.5, not 0.050, so incorrect.

Step1: Apply proportion method

Let the percent be \( p \). Using $\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}$, here part is 700, whole is 50, so $\frac{700}{50}=\frac{p}{100}$.

Step2: Solve for \( p \)

Cross - multiply: \( 50p=700\times100 \). Then \( p=\frac{700\times100}{50} \). Calculate \( 700\times100 = 70000 \), then \( \frac{70000}{50}=1400 \). So the percent is 1400%.

Answer:

\( \boldsymbol{\frac{50}{100}=\frac{30}{m}} \) (the third option: \( 50/100 = 30/m \))

Second Question (700 is what percent of 50?):