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Let's break down the information provided in the image:

1. The ratio of the present ages of Andy to Nancy is given as **7:10**.
2. We are tasked with finding the possible ratio of their ages three years ago (denoted by option (1)).
3. Additionally, we are given that the present ratio of the ages of Nancy to Chris is **5:4**, and we need to determine a ratio (denoted by option (2)) that is closest to the ratio of Andy's age to Chris's age based on this information.

### Let's solve step by step:

#### Step 1: Ratio of Andy to Nancy’s ages three years ago
The present ratio of Andy to Nancy is **7:10**. If we subtract three years from both their ages and form a new ratio, the ratio will change slightly.

We are given some options for this new ratio in the table (option (1)). The most logical choice will depend on their respective ages decreasing equally by 3 years. For now, let's hold off on the exact calculation and analyze based on proximity to the current ratio. Let's check the ratios:

- 7:9 (option 1) seems possible because subtracting from Nancy's larger age might bring them closer.
  
#### Step 2: Ratio of Andy to Chris's ages
We know Nancy’s current age is in the ratio **5:4** with Chris, and Andy’s age is in the ratio **7:10** with Nancy. To find the ratio of Andy to Chris’s ages, we can combine these ratios.

- Nancy/Chris = 5:4.
- Andy/Nancy = 7:10.

To compare Andy's and Chris’s ages, we multiply the ratios:

\[
\frac{\text{Andy}}{\text{Chris}} = \frac{\text{Andy}}{\text{Nancy}} \times \frac{\text{Nancy}}{\text{Chris}} = \frac{7}{10} \times \frac{5}{4} = \frac{35}{40} = \frac{7}{8}.
\]

So, the closest ratio for Andy to Chris’s ages (option (2)) would be **7:8**, which is closest to **3:4**.

### Final Selections:
- For (1), the closest choice would be **7:9**.
- For (2), the closest choice would be **3:4**.

Would you like more details on this approach or further explanations?

### Relative Questions:
1. How does age subtraction affect the ratio of two numbers?
2. What are the steps to simplify complex ratio problems involving three people?
3. How do ratios behave when adding or subtracting the same amount from both terms?
4. How can we calculate ratios if we know the proportional relationship between two people and need a third?
5. What are some real-life applications of using ratios in age or time problems?

### Tip:
When working with ratios, it is often helpful to convert them into fractions and perform algebraic operations on the fractions to compare or adjust the ratios based on changes like age shifts.

The ratio of the present ages of Andy to that of Nancy is 7:10. (1) _____ can be the possible ratio of their ages three years ago. If the ratio of the present ages of Nancy to that of Chris is 5:4, then which of the ratio in the given selection would be closest to that of the ratio of the present ages of Andy to that of Chris. (2) _____.

Explore how to solve a ratio problem involving the ages of Andy, Nancy, and Chris. This problem covers key concepts of proportions and age-related ratio transformations. Suitable for high school students in Grades 9-10.

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