Math / Algebra

QuestionThe Sugar Sweet Company is going to transport its sugar to market. It will cost $\$ 4500$ to rent trucks plus $\$ 225$ for each ton of sugar transported. The total cost, $C$ (in dollars), for transporting $n$ tons is given by the following function. $C(n)=4500+225 n$
Answer the following questions. (a) If the total cost is $\$ 9900$ , how many tons is the company transporting? $\square$ tons (b) What is the total cost of transporting 12 tons? \$7200

Studdy Solution

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.
$C(12) = 4500 + 225 \times 12$

STEP 7

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

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Studdy Solution

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.
$C(12) = 4500 + 225 \times 12$

STEP 7

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

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Studdy Solution

STEP 1

1. The cost function for transporting sugar is given as C(n)=4500+225n C(n) = 4500 + 225n 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 4500 + 225n = 9900 4500+225n=9900

STEP 4

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

STEP 5

Divide both sides by 225 to solve for n n n.n=5400225 n = \frac{5400}{225} n=2255400​ n=24 n = 24 n=24The company is transporting 24 \boxed{24} 24​ tons.

STEP 6

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

STEP 7

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

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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.

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

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

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

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

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 $\boxed{7200}$ .