the sugar sweet company is going to transport its sugar to market. it will cost $4500 to rent trucks plus…

the sugar sweet company is going to transport its sugar to market. it will cost $4500 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. c(n)=125n + 4500. answer the following questions. (a) what is the total cost of transporting 13 tons? $ (b) if the total cost is $7625, how many tons is the company transporting? tons

the sugar sweet company is going to transport its sugar to market. it will cost $4500 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. c(n)=125n + 4500. answer the following questions. (a) what is the total cost of transporting 13 tons? $ (b) if the total cost is $7625, how many tons is the company transporting? tons

Answer

Explanation:

Step1: Substitute $n = 13$ into cost - function

Substitute $n = 13$ into $C(n)=125n + 4500$. $C(13)=125\times13 + 4500$

Step2: Calculate the product

First, calculate $125\times13=1625$. $C(13)=1625 + 4500$

Step3: Calculate the sum

Then, calculate $1625+4500 = 6125$. $C(13)=6125$

Step4: Solve for $n$ when $C(n)=7625$

Set $C(n)=7625$ in the equation $C(n)=125n + 4500$. $7625=125n + 4500$

Step5: Isolate the term with $n$

Subtract 4500 from both sides of the equation. $7625−4500=125n$, so $3125 = 125n$

Step6: Solve for $n$

Divide both sides by 125. $n=\frac{3125}{125}=25$

Answer:

(a) $6125$ (b) $25$