A company that makes​ hair-care products had 7 comma 000 people try a new shampoo. Of the 7 comma 000 ​people, 42 had a mild allergic reaction. What percent of the people had a mild allergic​ reaction?

Question

Question content area bottom
Part 1
Write the percent proportion.
StartFraction 42 Over 7 comma 000 EndFraction
equalsStartFraction p Over 100 EndFraction
  
Part 2
Solve.
percentequals
  
enter your response here​%
​(Type an integer or a​ decimal.)

Answer 1

To find the percentage of people who had a mild allergic reaction, we can set up the percent proportion as follows:

Part 1: Percent Proportion \[ \frac{42}{7000} = \frac{p}{100} \]

Part 2: Solve for \(p\)

Now, we will solve for \(p\) by cross-multiplying:

\[ 42 \cdot 100 = 7000 \cdot p \]

This simplifies to:

\[ 4200 = 7000p \]

Next, divide both sides by 7000 to isolate \(p\):

\[ p = \frac{4200}{7000} \]

Now we can calculate \(p\):

\[ p = 0.6 \]

To convert it to a percentage, we multiply by 100:

\[ p = 0.6 \cdot 100 = 60 \]

Thus, the percentage of people who had a mild allergic reaction is:

\[ \text{percent} = 60% \]

So the answer to input is:

Part 2: percent equals 60%.