Part 1 of 3 If 10 miles \( \approx 16 \mathrm{~km} \), about how many miles Complete the ratio that can be used to sol \( \frac{\square \text { miles }}{16 \mathrm{~km}}=\frac{\text { ? miles }}{116 \mathrm{~km}} \) (

To solve the problem, we need to establish a ratio based on the given information that 10 miles is approximately equal to 16 kilometers. 1. **Extract known conditions:** - \( 10 \text{ miles} \approx 16 \text{ km} \) 2. **Set up the ratio:** We want to complete the ratio: \[ \frac{\square \text{ miles}}{16 \text{ km}} = \frac{\text{? miles}}{116 \text{ km}} \] 3. **Determine the conversion factor:** From the known condition, we can find how many miles correspond to 1 kilometer: \[ \frac{10 \text{ miles}}{16 \text{ km}} = \frac{5}{8} \text{ miles per km} \] 4. **Calculate the number of miles for 116 km:** To find the number of miles corresponding to 116 km, we can set up the equation: \[ \text{miles} = 116 \text{ km} \times \frac{5 \text{ miles}}{8 \text{ km}} \] Now, let's calculate this value. \[ \text{miles} = 116 \times \frac{5}{8} \] I'll perform the calculation now. Calculate the value by following steps: - step0: Calculate: \(116\times \frac{5}{8}\) - step1: Reduce the numbers: \(29\times \frac{5}{2}\) - step2: Multiply: \(\frac{29\times 5}{2}\) - step3: Multiply: \(\frac{145}{2}\) The calculation gives us: \[ \text{miles} = 116 \times \frac{5}{8} = 72.5 \text{ miles} \] 5. **Complete the ratio:** Now we can fill in the ratio: \[ \frac{72.5 \text{ miles}}{16 \text{ km}} = \frac{72.5 \text{ miles}}{116 \text{ km}} \] Thus, the completed ratio is: \[ \frac{72.5 \text{ miles}}{16 \text{ km}} = \frac{? \text{ miles}}{116 \text{ km}} \] where \( ? \text{ miles} = 72.5 \text{ miles} \).