Subjects algebra

Rainfall Prediction 2B81Ce

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1. **State the problem:** Sussex County received 43 inches of rainfall this year. The meteorologist's prediction had a percent error of about 18.02%. We need to find two possible values for the meteorologist's prediction. 2. **Formula for percent error:** $$\text{Percent Error} = \frac{|\text{Prediction} - \text{Actual}|}{\text{Actual}} \times 100\%$$ 3. **Set up the equation:** Let the prediction be $P$. The actual rainfall is 43 inches, and the percent error is 18.02%, so: $$18.02 = \frac{|P - 43|}{43} \times 100$$ 4. **Solve for $|P - 43|$:** $$\frac{|P - 43|}{43} = \frac{18.02}{100} = 0.1802$$ 5. **Multiply both sides by 43:** $$|P - 43| = 43 \times 0.1802 = 7.7486$$ 6. **Write the absolute value equation as two cases:** $$P - 43 = 7.7486 \quad \text{or} \quad P - 43 = -7.7486$$ 7. **Solve each case:** $$P = 43 + 7.7486 = 50.7486$$ $$P = 43 - 7.7486 = 35.2514$$ 8. **Final answer:** The two possible predictions are approximately $50.75$ inches and $35.25$ inches.