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%.