To meet a government requirement, a bottler must test 5 percent of its spring water and 10 percent of its sparkling water for purity. If a customer ordered 120 cases of spring water and 80 cases of sparkling water, then what percent of all the cases must the bottler test before he can send it out?

Concept & Logic Calculate the exact quantities of each component to find the overall percentage, using a weighted average logic. $$ \text{Overall \%} = \frac{\text{Total Tested}}{\text{Total Cases}} \times 100 $$ Step-by-Step Solution * Given: $120$ cases of spring water, $80$ cases of sparkling water. Total cases = $200$. * Tested spring water = $5\%$ of $120$ = $6$ cases. * Tested sparkling water = $10\%$ of $80$ = $8$ cases. * Total cases tested = $6 + 8 = 14$. * Required percentage = $\frac{14}{200} \times 100 = 7\%$. Exam Strategy & Shortcut Use the weighted average method directly: $\frac{120 \times 5 + 80 \times 10}{200} = \frac{600 + 800}{200} = 7\%$. This skips finding individual case numbers and goes straight to the ratio. Common Pitfall Simply averaging the percentages $(5\% + 10\%) / 2 = 7.5\%$ without accounting for the different case volumes. Always weight percentages by their respective base quantities. Final Answer Therefore, the correct answer is **7.0%**.