Math Snap

STEP 1

1. The cost function for transporting sugar is given as $C(n) = 4500 + 225n$.
2. We need to find the number of tons transported when the total cost is $9900.
3. We need to find the total cost when 12 tons are transported.

STEP 2

1. Solve for the number of tons transported when the total cost is $9900.
2. Calculate the total cost of transporting 12 tons.

STEP 3

To find the number of tons transported when the total cost is $9900, set \( C(n) = 9900 \) and solve for \( n \).
$$4500 + 225n = 9900$$

STEP 4

Subtract 4500 from both sides to isolate the term with $n$.
$$225n = 9900 - 4500$$ $$225n = 5400$$

STEP 5

Divide both sides by 225 to solve for $n$.
$$n = \frac{5400}{225}$$ $$n = 24$$ The company is transporting $\boxed{24}$ tons.

STEP 6

To find the total cost of transporting 12 tons, substitute $n = 12$ into the cost function.
$$C(12) = 4500 + 225 \times 12$$

Calculate the expression.
$$C(12) = 4500 + 2700$$ $$C(12) = 7200$$ The total cost of transporting 12 tons is $\boxed{7200}$.