A bag of a dozen grapefruit was selling for $6.60. The produce manager added some grapefruit to the bag but did not change the $6.60 price. The price of a dozen grapefruit now was actually $4.40. How many grapefruit were added to the bag?

Let's break down the problem step by step:

1. Initially, a dozen (12) grapefruit were sold for $6.60. The price per grapefruit is:
   \[
   \text{Price per grapefruit} = \frac{6.60}{12} = 0.55 \, \text{dollars}.
   \]

2. After adding some grapefruit to the bag, the price of a dozen grapefruit (12) became $4.40. This means the price per grapefruit is now:
   \[
   \text{New price per grapefruit} = \frac{4.40}{12} \approx 0.3667 \, \text{dollars}.
   \]

3. The total price for the entire bag remains $6.60, so if we let $ x $ represent the total number of grapefruit in the new bag, then:
   \[
   \frac{6.60}{x} = 0.3667.
   \]

4. Solving for $ x $:
   \[
   x = \frac{6.60}{0.3667} \approx 18.
   \]

So, there are now 18 grapefruit in the bag.

5. The number of grapefruit added to the original 12 is:
   \[
   18 - 12 = 6.
   \]

Thus, **6 grapefruit** were added to the bag.

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Would you like further clarification or more details on any part of the solution?

Here are five related questions to expand your understanding:

1. How would the price change if the bag now contained 20 grapefruit but still cost $6.60?
2. What if the price of a dozen grapefruit decreased to $3.60, how many grapefruit would have been added to the bag?
3. If the price per grapefruit increased instead of decreasing, what would be the effect on the number of grapefruit added?
4. How would this problem change if the bag initially contained a different number of grapefruit, say 10 instead of 12?
5. What is the total weight of the bag if each grapefruit weighs 0.5 kg?

**Tip**: When solving proportion problems, always ensure you're clear about what remains constant (in this case, total price) and what changes (quantity or price per unit).

Discover how to solve a real-world problem involving proportions and unit price calculations. A dozen grapefruit initially sold for $6.60, but after adding more grapefruit to the bag without changing the price, the cost per dozen became $4.40. Learn step-by-step how to find out how many grapefruit were added to the bag. This problem is suitable for Grades 5-7.

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