Question

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 content area bottom
Part 1
Write the percent proportion.
StartFraction 42 Over 7 comma 000 EndFraction
equalsStartFraction p Over nothing EndFraction

Answer 1

To calculate the percent of people who had a mild allergic reaction, we can set up the proportion you mentioned:

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

Here, \( p \) represents the percentage of people who experienced a mild allergic reaction. To find \( p \), we can cross-multiply and solve for \( p \):

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

This simplifies to:

\[
4200 = 7000p
\]

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

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

Calculating this gives:

\[
p = 0.6
\]

To find the percentage, we multiply by 100:

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

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