1. **State the problem:** We have a table with two days, Monday and Tuesday, showing numbers of flies and mosquitoes. We know Monday has 15 flies and Tuesday has 14 mosquitoes. We need to find the missing values: mosquitoes on Monday and flies on Tuesday. 2. **Understand the ratio:** The problem implies the ratio of flies to mosquitoes is constant for both days. Let the ratio be $\frac{\text{Flies}}{\text{Mosquitoes}} = k$. 3. **Set up the ratio for Monday:** Given Monday has 15 flies and unknown mosquitoes $m$, the ratio is: $$\frac{15}{m} = k$$ 4. **Set up the ratio for Tuesday:** Given Tuesday has unknown flies $f$ and 14 mosquitoes, the ratio is: $$\frac{f}{14} = k$$ 5. **Equate the ratios:** Since the ratio $k$ is the same for both days, $$\frac{15}{m} = \frac{f}{14}$$ 6. **Express $f$ in terms of $m$:** Cross-multiply: $$15 \times 14 = m \times f$$ $$210 = m f$$ 7. **Use the ratio to find values:** From step 3, $k = \frac{15}{m}$. From step 4, $f = 14k = 14 \times \frac{15}{m} = \frac{210}{m}$. 8. **Solve for $m$ and $f$:** Since $f = \frac{210}{m}$ and $m f = 210$, the values satisfy the equation. To find integer values, consider factors of 210. Since Monday mosquitoes $m$ must be an integer, try $m=14$: - Then $f = \frac{210}{14} = 15$. 9. **Check the ratio:** For Monday: $$\frac{15}{14} \approx 1.0714$$ For Tuesday: $$\frac{15}{14} \approx 1.0714$$ Ratios match. 10. **Final answer:** - Monday mosquitoes = 14 - Tuesday flies = 15 Thus, the completed table is: | Day | Flies | Mosquitoes | |---------|-------|------------| | Monday | 15 | 14 | | Tuesday | 15 | 14 |