Subjects algebra

Ratio Table

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Ratio Table


1. **State the problem:** We are given a ratio table with paired values where the ratios are consistent. The table is: | 20 | 7 | | 40 | ? | | ? | 21 | | 80 | 28 | | 100| ? | We need to find the missing values maintaining the ratio. 2. **Identify the ratio:** The first pair is $20$ and $7$, so the ratio is $$\frac{20}{7}$$. 3. **Calculate missing value in row 2:** Given $40$ in the first column, find the second column value using the ratio: $$\text{Second value} = \frac{7}{20} \times 40 = 14$$ 4. **Calculate missing value in row 3:** Given $21$ in the second column, find the first column value using the ratio: $$\text{First value} = \frac{20}{7} \times 21 = 60$$ 5. **Check given values in row 4:** Given $80$ and $28$, check ratio: $$\frac{80}{28} = \frac{20}{7}$$ correct. 6. **Calculate missing value in row 5:** Given $100$ in the first column, find the second column value: $$\text{Second value} = \frac{7}{20} \times 100 = 35$$ 7. **Complete table:** | 20 | 7 | | 40 | 14 | | 60 | 21 | | 80 | 28 | | 100| 35 | **Final answer:** The missing values are 14, 60, and 35.