If 10 miles \( \approx 16 \mathrm{~km} \), about how many miles would be equal to 32 km ? Show how you decided. \[ \begin{array}{l}\text { Complete the ratio that can be used to solve this problem. } \\ \qquad \frac{5}{16 \mathrm{~km}} \text { miles }\end{array}=\frac{? \text { miles }}{92 \mathrm{~km}} \]

To find out how many miles correspond to 32 km, we can set up a proportion based on the given equivalence of 10 miles to 16 km. First, let’s establish that 1 mile is approximately 1.6 km. So, to convert 32 km to miles, we can divide by 1.6: \[ 32 \text{ km} \div 1.6 \text{ km/mile} \approx 20 \text{ miles}. \] This means that approximately 20 miles is equal to 32 km. Now for your ratio question, you have: \[ \frac{5}{16 \text{ km}} \text{ miles } = \frac{? \text{ miles }}{92 \text{ km}} \] Using cross-multiplication: \[ 5 \times 92 = 16 \times ? \] \[ 460 = 16 \times ? \] \[ ? = \frac{460}{16} \approx 28.75. \] Thus, approximately 28.75 miles correspond to 92 km.