1. The problem asks us to find three ratios equivalent to $8 : 20$. 2. Two ratios are equivalent if their fractions are equal. The ratio $8 : 20$ can be written as the fraction $\frac{8}{20}$. 3. Simplify $\frac{8}{20}$ by dividing numerator and denominator by their greatest common divisor, which is 4: $$\frac{8 \div 4}{20 \div 4} = \frac{2}{5}$$ 4. Now, check each option by converting the ratio to a fraction and simplifying if needed: - A: $1 : 4 = \frac{1}{4}$ (not equal to $\frac{2}{5}$) - B: $4 : 10 = \frac{4}{10} = \frac{2}{5}$ (equivalent) - C: $24 : 60 = \frac{24}{60} = \frac{2}{5}$ (equivalent) - D: $2 : 5 = \frac{2}{5}$ (equivalent) - E: $10 : 24 = \frac{10}{24} = \frac{5}{12}$ (not equivalent) 5. Therefore, the three equivalent ratios are B, C, and D.