1. The problem asks us to find three ratios equivalent to $5 : 2$. 2. Two ratios are equivalent if their fractions are equal. The ratio $5 : 2$ can be written as the fraction $\frac{5}{2}$. 3. We check each option by converting the ratio to a fraction and comparing it to $\frac{5}{2}$. - A: $2 : 5 = \frac{2}{5}$, which is not equal to $\frac{5}{2}$. - B: $10 : 4 = \frac{10}{4} = \frac{5}{2}$, equivalent. - C: $20 : 50 = \frac{20}{50} = \frac{2}{5}$, not equivalent. - D: $35 : 14 = \frac{35}{14} = \frac{5}{2}$, equivalent. - E: $55 : 22 = \frac{55}{22} = \frac{5}{2}$, equivalent. 4. Therefore, the three equivalent ratios to $5 : 2$ are B, D, and E.