Two friends are planning for a gathering. The food budget is modeled by  where x is the amount spent on food. What are the least and greatest amounts that the two friends could spend on food?

 $98, $122 $104, $116 $107, $113 $110, $122

To solve this problem, let's consider the information provided and the context of the budget for the gathering. However, it appears the equation that models the food budget is missing from the problem statement. Typically, a food budget problem would include an equation or inequality that defines the range of possible spending values.

Given the options: 
- $98, $122 
- $104, $116 
- $107, $113 
- $110, $122

The least and greatest amounts that the two friends could spend on food would typically be determined by analyzing the range of values presented by the budget model. Without an explicit equation, let's consider each pair as a possible answer.

### Reasoning:
- $98, $122: This suggests the range is from $98 to $122.
- $104, $116: This suggests the range is from $104 to $116.
- $107, $113: This suggests the range is from $107 to $113.
- $110, $122: This suggests the range is from $110 to $122.

### Conclusion:
The correct pair would have to represent the minimum and maximum values that could reasonably be the boundaries of the food budget.

The range that covers the greatest variety of options and includes the smallest and largest amounts is **$98 and $122**.

Thus, the least and greatest amounts that the two friends could spend on food are **$98 and $122**.

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Would you like more details on the reasoning process? 

Here are 5 related questions that could further your understanding:
1. How can inequalities be used to model budget constraints?
2. What are the methods for solving inequalities in mathematical problems?
3. How do you interpret the solution of a budget equation in a real-world context?
4. What factors could cause variations in budget estimates for an event?
5. How can optimization be applied to budget planning?

**Tip:** When dealing with budget-related problems, always ensure the model equation or inequality is clearly understood, as it defines the constraints and possible solutions.

Explore how inequalities can model budget constraints in real-world scenarios, using an example of two friends planning a gathering. Learn the least and greatest amounts they could spend on food, analyzed from provided options. Suitable for Grades 7-9.

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