Keddy, Cheko and Miko have saved some allowance to buy a gift for their mother. Keddy and Cheko have $329. Keddy and Miko have $529. The ratio of Cheko to Miko's savings is 2 : 7. How much does Keddy have?

Let's denote the savings of Keddy, Cheko, and Miko as $K$, $C$, and $M$ respectively.

1. From the problem, we have the following equations: $K + C = 329$ $K + M = 529$

2. We are also given the ratio of Cheko to Miko's savings: $\frac{C}{M} = \frac{2}{7}$ This implies: $7C = 2M \quad \text{or} \quad M = \frac{7}{2}C$

3. Substitute $M$ from the ratio into the second equation: $K + \frac{7}{2}C = 529$

4. Now we have two equations: $K + C = 329 \quad \text{(Equation 1)}$ $K + \frac{7}{2}C = 529 \quad \text{(Equation 2)}$

5. Subtract Equation 1 from Equation 2 to eliminate $K$: $\left( K + \frac{7}{2}C \right) - (K + C) = 529 - 329$ $\frac{7}{2}C - C = 200$ $\frac{5}{2}C = 200$ $C = 200 \times \frac{2}{5}$ $C = 80$

6. Substitute $C = 80$ back into Equation 1 to find $K$: $K + 80 = 329$ $K = 329 - 80$ $K = 249$

Therefore, Keddy has $249.