The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks plus $125 for each ton of sugar transported. The total cost, C (in dollars), for transporting N tons is given by the following function.

Question

C(n)=3500+125n
what is the total cost of transporting 14 tons
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If the total cost is $6625, how many tons is the company transporting?
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Answer 1

To find the total cost of transporting 14 tons of sugar, we can use the provided cost function \( C(n) = 3500 + 125n \):

1. Calculate the total cost for 14 tons: \[ C(14) = 3500 + 125 \times 14 \] \[ C(14) = 3500 + 1750 \] \[ C(14) = 5250 \]

So, the total cost of transporting 14 tons is $5250.

2. To find out how many tons the company is transporting if the total cost is $6625, we set up the equation with the cost function: \[ C(n) = 3500 + 125n \] Set \( C(n) = 6625 \): \[ 6625 = 3500 + 125n \] Subtract \( 3500 \) from both sides: \[ 6625 - 3500 = 125n \] \[ 3125 = 125n \] Now, divide both sides by \( 125 \): \[ n = \frac{3125}{125} = 25 \]

So, if the total cost is $6625, the company is transporting 25 tons.