Question

the sugar sweet company is going to transport its sugar to market. it will cost $3500 to rent trucks plus $175 for each ton of sugar transported. the total cost, c (in dollars), for transporting n tons is given by the following function.
c(n) = 3500 + 175n
answer the following questions.
(a) what is the total cost of transporting 15 tons?
$
(b) if the total cost is $7700, how many tons is the company transporting?
tons

Explanation:

Part (a)

Step1: Identify the formula and input

The cost function is \( C(n) = 3500 + 175n \). We need to find \( C(15) \), so substitute \( n = 15 \) into the formula.

Step2: Calculate the cost

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Step1: Set up the equation

We know \( C(n)=7700 \) and \( C(n)=3500 + 175n \). So set \( 3500 + 175n=7700 \).

Step2: Solve for \( n \)

Subtract 3500 from both sides: \( 175n=7700 - 3500=4200 \). Then divide both sides by 175: \( n=\frac{4200}{175} = 24 \).

Answer:

The total cost of transporting 15 tons is \(\$6125\).

Part (b)