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Part 1
A company that makes​ hair-care products had 9 comma 000 people try a new shampoo. Of the 9 comma 000 ​people, 54 had a mild allergic reaction. What percent of the people had a mild allergic​ reaction?
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Part 1
Write the percent proportion.
StartFraction 54 Over 9 comma 000 EndFraction
equalsStartFraction p Over nothing EndFraction

1 answer

To find the percentage of people who had a mild allergic reaction to the new shampoo, you would set up the percentage proportion as you indicated. The proportion can be written as:

\[ \frac{54}{9000} = \frac{p}{100} \]

where \( p \) represents the percentage of people who had a mild allergic reaction.

To solve for \( p \), cross-multiply:

\[ 54 \times 100 = p \times 9000 \]

This simplifies to:

\[ 5400 = p \times 9000 \]

Next, divide both sides by 9000 to isolate \( p \):

\[ p = \frac{5400}{9000} \]

Calculating that gives:

\[ p = 0.6 \]

To convert this to a percentage, multiply by 100:

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

Therefore, \( 60% \) of the people had a mild allergic reaction.

So the answer to the original question is:

\[ 60% \]

The complete proportion you set up is:

\[ \frac{54}{9000} = \frac{60}{100} \]

This indicates that 60 out of every 100 people (or 60%) had a mild allergic reaction.