1. **State the problem:** Mrs. Sanchez spent 19.14 on filters and will receive a 5% rebate. We need to find the final price after applying the rebate. 2. **Formula:** The final price after a rebate is calculated as: $$\text{Final Price} = \text{Original Price} - (\text{Rebate Percentage} \times \text{Original Price})$$ 3. **Calculate the rebate amount:** $$\text{Rebate} = 0.05 \times 19.14 = 0.957$$ 4. **Calculate the final price:** $$\text{Final Price} = 19.14 - 0.957$$ 5. **Simplify the subtraction:** $$\text{Final Price} = 19.14 - 0.957 = 18.183$$ 6. **Round to two decimal places:** $$\text{Final Price} \approx 18.18$$ 7. **Compare with given options:** Neither 17.21 nor 22.42 matches 18.18, so the correct final price after rebate is approximately 18.18, which is not listed among the options. **Final answer:** The final price after the 5% rebate is approximately $18.18.