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The problem shown asks about how many large candles can be bought given a budget and some constraints.

Here’s a breakdown of the question:
- A small business owner has a **$2,200 budget**.
- The owner must purchase a **minimum of 200 candles** to maintain the discounted pricing.
- The small candles cost **$4.90 each**.
- The large candles cost **$11.60 each**.
- The objective is to find out the maximum number of large candles the owner can purchase while staying within the budget and maintaining the minimum total of 200 candles.

### Step-by-Step Solution:
Let:
- $ x $ = number of small candles purchased.
- $ y $ = number of large candles purchased.

We need to satisfy the following conditions:
1. $ x + y = 200 $ (The total number of candles must be at least 200).
2. The total cost must not exceed the budget: $ 4.90x + 11.60y \leq 2200 $.

Using equation (1), $ x = 200 - y $. 

Substitute $ x $ in the second equation:

\[
4.90(200 - y) + 11.60y \leq 2200
\]

Now, solve for $ y $. 

I'll calculate this next.The maximum number of large candles that the owner can purchase is approximately **182**. 

If the owner buys 182 large candles, they would need to purchase $ 200 - 182 = 18 $ small candles to maintain the total count of 200 candles and stay within the budget.

Would you like further details or explanations about this calculation? Here are a few related questions for practice:

1. What would the budget need to be if the owner wanted to buy 190 large candles?
2. How many candles can the owner buy if all of them are small?
3. What is the minimum number of large candles the owner could buy while still purchasing at least 200 candles?
4. How does the total cost change if the price of small candles increases to $5.00 each?
5. What happens to the maximum number of large candles if the budget is reduced by $200?

**Tip:** When solving problems involving a budget, ensure that all conditions (such as minimum purchases) are factored in, so your solution satisfies every constraint.

A small business owner budgets $2,200 to purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

Explore how to determine the maximum number of large candles a small business owner can purchase within a $2,200 budget while fulfilling a minimum purchase requirement. This problem involves solving a system of linear inequalities, suitable for high school students learning algebra.

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