Subjects algebra

Percent Allergic

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1. **State the problem:** We need to find what percent of 5,000 people had a mild allergic reaction if 30 people reacted. 2. **Write the proportion:** The problem gives the proportion $$\frac{30}{5000} = \frac{p}{100}$$ where $p$ is the percent we want to find. 3. **Explain the proportion:** This proportion compares the part to the whole (30 out of 5000) and sets it equal to the percent $p$ out of 100. 4. **Solve for $p$:** Cross multiply to get: $$30 \times 100 = 5000 \times p$$ $$3000 = 5000p$$ 5. **Isolate $p$:** $$p = \frac{3000}{5000}$$ 6. **Simplify:** $$p = 0.6$$ 7. **Interpret the result:** The percent of people who had a mild allergic reaction is $0.6\%$. **Final answer:** $0.6\%$ of the people had a mild allergic reaction.