Subjects algebra

Ratio Table 895992

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1. **State the problem:** We have a ratio table with two columns and five rows. Some values are missing, represented by squares (□). We need to find these missing values to complete the table. 2. **Given table:** $$\begin{array}{cc} 11 & \square \\ 33 & 9 \\ 66 & 18 \\ 77 & 21 \\ 88 & \square \\ \end{array}$$ 3. **Identify the ratio:** The second row gives us a known ratio: $33$ corresponds to $9$. We can find the ratio between the first and second columns by dividing: $$\text{ratio} = \frac{9}{33} = \frac{3}{11}$$ 4. **Use the ratio to find missing values:** - For the first row, the first column is $11$. Using the ratio $\frac{3}{11}$, the second column value is: $$11 \times \frac{3}{11} = \cancel{11} \times \frac{3}{\cancel{11}} = 3$$ - For the last row, the first column is $88$. Using the ratio $\frac{3}{11}$, the second column value is: $$88 \times \frac{3}{11} = \cancel{88} \times \frac{3}{\cancel{11}} = 8 \times 3 = 24$$ 5. **Verify other values:** - $66 \times \frac{3}{11} = 18$ (given) - $77 \times \frac{3}{11} = 21$ (given) 6. **Final completed table:** $$\begin{array}{cc} 11 & 3 \\ 33 & 9 \\ 66 & 18 \\ 77 & 21 \\ 88 & 24 \\ \end{array}$$ **Answer:** The missing values are $3$ and $24$.