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Let's go through the given information and solve the questions.

The total cost function is given by:

\[
C(n) = 150n + 6500
\]

where:
- $ C(n) $ is the total cost in dollars for transporting $ n $ tons of sugar.
- The fixed cost is $6500 (for renting trucks).
- The variable cost is $150 per ton of sugar transported.

### Part (a) 
We are asked to find how many tons are being transported if the total cost is $10,100. 

We know:

\[
C(n) = 150n + 6500
\]

Substitute $ C(n) = 10100 $:

\[
10100 = 150n + 6500
\]

Solve for $ n $:

\[
10100 - 6500 = 150n
\]
\[
3600 = 150n
\]
\[
n = \frac{3600}{150} = 24
\]

So, the company is transporting **24 tons** of sugar.

### Part (b) 
We are asked to find the total cost for transporting 11 tons.

Substitute $ n = 11 $ into the cost function:

\[
C(11) = 150(11) + 6500
\]
\[
C(11) = 1650 + 6500
\]
\[
C(11) = 8150
\]

So, the total cost of transporting 11 tons is **$8,150**.

---

Would you like a detailed explanation of any of these steps?

Here are some related questions:
1. How would the cost change if the company transported 30 tons?
2. What is the fixed cost's contribution to the total cost?
3. How many tons would result in a total cost of $12,000?
4. What is the marginal cost per ton of sugar?
5. How can you graph the cost function and interpret its slope?

**Tip**: Always isolate the variable when solving equations, and check by substituting your solution back into the original formula.

The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $150 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function: C(n) = 150n + 6500. 
(a) If the total cost is $10,100, how many tons is the company transporting?
(b) What is the total cost of transporting 11 tons?

Learn how to solve linear cost function problems involving transportation costs for sugar. This example includes calculating the total cost of transporting sugar and finding the number of tons based on a given total cost. Suitable for students in Grades 7-9.

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