A company that makes​ hair-care products had 6 comma 000 people try a new shampoo. Of the 6 comma 000 ​people, 48 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 48 Over 6 comma 000 EndFraction
equalsStartFraction p Over nothing EndFraction

Answer 1

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

\[ \frac{48}{6000} = \frac{p}{100} \]

Now, we can solve for \( p \), which represents the percentage of people with a mild allergic reaction.

1. Cross-multiply to solve for \( p \): \[ 48 \times 100 = 6000 \times p \] \[ 4800 = 6000p \]

2. Divide both sides by 6000 to isolate \( p \): \[ p = \frac{4800}{6000} \]

3. Simplify the fraction: \[ p = \frac{48}{60} = \frac{4}{5} = 0.8 \]

4. Convert to a percentage by multiplying by 100: \[ p = 0.8 \times 100 = 80% \]

So, the percent of the people who had a mild allergic reaction is 0.8%.