1. **State the problem:** Tamika pays 5.50 to send 110 text messages. We want to find the cost to send 52 text messages. 2. **Identify the formula:** Since cost is proportional to the number of messages, we use the ratio formula: $$\frac{\text{Cost}_1}{\text{Messages}_1} = \frac{\text{Cost}_2}{\text{Messages}_2}$$ 3. **Plug in known values:** $$\frac{5.50}{110} = \frac{x}{52}$$ 4. **Solve for $x$:** Multiply both sides by 52: $$x = \frac{5.50}{110} \times 52$$ 5. **Simplify the fraction:** $$\frac{5.50}{110} = \frac{\cancel{5.50}}{\cancel{110}} = 0.05$$ 6. **Calculate $x$:** $$x = 0.05 \times 52 = 2.6$$ 7. **Answer:** It would cost **2.6** to send 52 text messages.