The ratio of the number of miles Sophia ran to the number of miles Mia ran is given as $2:3$. This means for every 2 miles Sophia ran, Mia ran 3 miles.

Mia ran 12 miles, and we need to determine how far Sophia ran. To solve this:

1. Write the ratio as a fraction: $\frac{\text{Sophia's miles}}{\text{Mia's miles}} = \frac{2}{3}$

2. Substitute the known value for Mia's miles (12 miles): $\frac{\text{Sophia's miles}}{12} = \frac{2}{3}$

3. Solve for Sophia's miles by cross-multiplying: $\text{Sophia's miles} = \frac{2}{3} \times 12 = 8$

Sophia ran 8 miles.

Would you like more details or have any questions?

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Related Questions:

1. What if Mia ran 18 miles? How far would Sophia have run?
2. How can ratios be applied to solve similar real-world problems?
3. What is the proportional relationship between Sophia's and Mia's running distances?
4. How would the ratio change if Sophia ran 16 miles while Mia ran 24 miles?
5. What is a step-by-step method for checking your work when solving ratio problems?

Tip:

When working with ratios, always remember to simplify or scale the ratio proportionally to match the given values.