if these are the 
Product Prices 

 450.00 
 599.00 
 580.00 
 300.00 
 580.00 
 450.00 
 550.00 
 150.00 
 200.00 
 300.00 
 450.00 
 550.00 
 150.00 
 450.00 
 599.00 
 450.00 
 200.00 
 150.00 
 150.00 
 599.00 
 300.00 

how much quantity would i need to add to make a total of 75975

To find the quantity needed to reach a total sum of **75,975** from the given product prices, we'll calculate the current sum of the prices and then determine how much more is needed to reach the target total. Here are the steps:

1. **Calculate the total sum of the current product prices.**
2. **Subtract this sum from the target total of 75,975 to find the remaining amount needed.**
3. **Divide the remaining amount by the average price of the products to estimate the quantity needed.**

### Step-by-Step Calculation

#### 1. Calculate the total sum of the current product prices:

Let's add up all the provided product prices:

\[
450.00 + 599.00 + 580.00 + 300.00 + 580.00 + 450.00 + 550.00 + 150.00 + 200.00 + 300.00 + 450.00 + 550.00 + 150.00 + 450.00 + 599.00 + 450.00 + 200.00 + 150.00 + 150.00 + 599.00 + 300.00
\]

#### 2. Sum the prices:
Let's calculate the sum of these values:

\[
450 + 599 + 580 + 300 + 580 + 450 + 550 + 150 + 200 + 300 + 450 + 550 + 150 + 450 + 599 + 450 + 200 + 150 + 150 + 599 + 300 = 8757
\]

The total sum of the product prices is **8,757**.

#### 3. Find the remaining amount needed:

Now, subtract the total sum of product prices from the target total of **75,975**:

\[
75,975 - 8,757 = 67,218
\]

So, you need an additional **67,218** to reach the target total.

#### 4. Estimate the quantity needed:

To estimate the quantity, we divide the remaining amount needed by the average price of the products. 

Let's first calculate the average price of the products:

\[
\text{Average Price} = \frac{\text{Total Sum of Prices}}{\text{Number of Prices}}
\]

There are 21 prices given:

\[
\text{Average Price} = \frac{8757}{21} \approx 416.05
\]

Now, calculate the quantity needed:

\[
\text{Quantity Needed} = \frac{\text{Remaining Amount Needed}}{\text{Average Price}}
\]

\[
\text{Quantity Needed} = \frac{67,218}{416.05} \approx 161.57
\]

Since you can't have a fraction of a product, you would need to add **162** more products at the average price to reach or exceed the total of **75,975**.

### Conclusion

You would need to add **162 products** at the average price to reach the total of **75,975**.

Would you like further details or have any questions?

#### Related Questions:
1. What is the minimum number of products required to exceed a total of 75,975 if all new products have the same maximum price in the list?
2. How would the required quantity change if the prices were doubled?
3. What if you could only add products at the lowest price on the list? How many would you need then?
4. How does the distribution of prices affect the average price?
5. How would the total change if you removed the three highest prices from the current list?

**Tip:** When working with financial data, always consider rounding rules and the impact of decimals on the final quantity needed.

Learn how to calculate the quantity needed to reach a total of 75,975 from given product prices. This problem involves arithmetic and summation concepts, where you'll use the total sum of product prices and average price calculation to determine the quantity required. Suitable for students in Grades 6-8.

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