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Math  /  Algebra

QuestionThe Sugar Sweet Company is going to transport its sugar to market. It will cost $4500\$ 4500 to rent trucks plus $225\$ 225 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function. C(n)=4500+225nC(n)=4500+225 n
Answer the following questions. (a) If the total cost is $9900\$ 9900, how many tons is the company transporting? □\square ns (b) What is the total cost of transporting 12 tons? \ \square$

Studdy Solution

STEP 1

1. The fixed cost for renting trucks is \$4500.
2. The variable cost per ton of sugar transported is \$225.
3. The total cost function is given by \( C(n) = 4500 + 225n \).
4. We need to solve for the number of tons when the total cost is \$9900.
5. We need to calculate the total cost for transporting 12 tons.

STEP 2

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

STEP 3

To find the number of tons when the total cost is \$9900, set up the equation from the cost function:
C(n)=4500+225n C(n) = 4500 + 225n
Substitute C(n)=9900 C(n) = 9900 :
9900=4500+225n 9900 = 4500 + 225n

STEP 4

Solve the equation for n n .
Subtract 4500 from both sides:
9900−4500=225n 9900 - 4500 = 225n 5400=225n 5400 = 225n

STEP 5

Divide both sides by 225 to solve for n n :
n=5400225 n = \frac{5400}{225} n=24 n = 24
The company is transporting 24\boxed{24} tons.

STEP 6

To find the total cost for transporting 12 tons, substitute n=12 n = 12 into the cost function:
C(12)=4500+225×12 C(12) = 4500 + 225 \times 12

STEP 7

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

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