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------------------------------------------------ The Sugar Sweet Company is going to transport its sugar to market. The cost [tex]C[/tex] (in dollars) of renting trucks for transporting [tex]n[/tex] tons is given by the following function:

[tex]C(n) = 5500 + 125n[/tex]

Answer the following questions:

(a) What is the total cost of transporting 12 tons?

[tex]\$ \square[/tex]

(b) If the total cost is [tex]\$8125[/tex], how many tons is the company transporting?

[tex]\square \text{ tons}[/tex]

Sure! Let's go through the questions step-by-step.

### (a) What is the total cost of transporting 12 tons?

To find the total cost of transporting 12 tons of sugar, we use the cost function provided:
[tex]\[ C(n) = 5500 + 125n \][/tex]
Here, [tex]$ n $[/tex] is the number of tons. We need to substitute [tex]$ n = 12 $[/tex] into the equation.

[tex]\[ C(12) = 5500 + 125 \times 12 \][/tex]

Calculate [tex]$ 125 \times 12 $[/tex]:
[tex]\[ 125 \times 12 = 1500 \][/tex]

Now, add this to the fixed cost of \[tex]$5500:
\[ C(12) = 5500 + 1500 = 7000 \]

So, the total cost of transporting 12 tons is \$[/tex]7000.

### (b) If the total cost is \[tex]$8125, how many tons is the company transporting?

Here, we have the total cost given as \$[/tex]8125, and we need to find the number of tons, [tex]$ n $[/tex].

Start with the cost equation:
[tex]\[ C(n) = 5500 + 125n = 8125 \][/tex]

First, subtract \$5500 from both sides to solve for the term with [tex]$ n $[/tex]:
[tex]\[ 125n = 8125 - 5500 \][/tex]

Calculate the right side:
[tex]\[ 8125 - 5500 = 2625 \][/tex]

Now, divide by 125 to find the number of tons:
[tex]\[ n = \frac{2625}{125} \][/tex]

Calculate the division:
[tex]\[ n = 21 \][/tex]

So, the company is transporting 21 tons.

These are the solutions to the given questions.