1. The problem asks if the ratios 6 staff members to 10 campers and 3 staff members to 5 campers are equivalent. 2. To check if two ratios are equivalent, we can write them as fractions and see if they simplify to the same value. 3. The first ratio is $\frac{6}{10}$. 4. The second ratio is $\frac{3}{5}$. 5. Simplify the first fraction by dividing numerator and denominator by their greatest common divisor, which is 2: $$\frac{6 \div 2}{10 \div 2} = \frac{3}{5}$$ 6. The simplified first ratio is $\frac{3}{5}$, which is exactly the second ratio. 7. Since both ratios simplify to the same fraction, they are equivalent. **Final answer:** Yes, the ratios are equivalent.