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 0.6 EndFraction

Answer 1

To find the percent of people who had a mild allergic reaction, you can set up the proportion based on the number of people who had reactions compared to the total number of people.

1. You already have the number of people who had a mild allergic reaction: 42.
2. The total number of people who tried the shampoo is 7,000.

You can calculate the percentage by using the following formula:

\[ \text{Percentage} = \left(\frac{\text{Number of people with reaction}}{\text{Total number of people}} \right) \times 100 \]

Plugging in the numbers:

\[ \text{Percentage} = \left(\frac{42}{7000}\right) \times 100 \]

Now, calculating it step-by-step:

1. Divide 42 by 7000:

\[ \frac{42}{7000} = 0.006 \]

2. Multiply by 100 to convert to a percentage:

\[ 0.006 \times 100 = 0.6 \]

So, 0.6% of the people had a mild allergic reaction.

Percent Proportion

The proportion you provided can be set up correctly as follows:

\[ \frac{42}{7000} = \frac{p}{100} \]

Then, let's solve for \( p \) (the percentage):

1. Cross-multiply:

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

This simplifies to:

\[ 4200 = 7000p \]

2. Now, divide both sides by 7000:

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

3. This simplifies to:

\[ p = 0.6 \]

Thus, the percent proportion that you mentioned is correct, leading to the conclusion that 0.6% of the people experienced a mild allergic reaction.