Math / Algebra

Question10 11 12
The Sugar sweet Company is going to transport its sugar to market. It will cost $\$ 3500$ to rent trucks, and it will cost an additional $\$ 175$ for each ton of sugar transported.
Let $C$ represent the total cost (in dollars), and let $S$ represent the amount of sugar (in tons) transported. Write an equation relating $C$ to $S$ . Then use this equation to find the total cost to transpyyt 12 tons of sugar.
Equation: $\square$
Total cost to transport 12 tons of sugar: $\square$ Check

Studdy Solution

STEP 1

What is this asking? We need to figure out the equation that connects the total cost of transporting sugar with the amount of sugar being transported, and then use that equation to calculate the total cost for transporting 12 tons of sugar. Watch out! Don't forget to include both the fixed cost of renting the trucks and the variable cost that depends on the amount of sugar.

STEP 2

1. Define the variables and their units.
2. Create the cost equation.
3. Calculate the cost for 12 tons.

STEP 3

Let's define what our variables represent. $C$ is the total cost in $\$$ , and $S$ is the amount of sugar transported in tons.

STEP 4

The total cost $C$ has two parts: the fixed cost of renting the trucks, which is $\$3500$ , and the variable cost, which depends on the amount of sugar $S$ .

STEP 5

The variable cost is $\$175$ per ton of sugar.
So, for $S$ tons of sugar, the variable cost is $175 \cdot S$ .

STEP 6

To get the total cost $C$ , we add the fixed cost and the variable cost: $C = 3500 + 175 \cdot S$ .
There's our equation!

STEP 7

Now, we want to find the total cost to transport 12 tons of sugar.
So, we'll substitute $S = 12$ into our equation: $C = 3500 + 175 \cdot 12$ .

STEP 8

Let's calculate that! $175 \cdot 12 = 2100$ .

STEP 9

So, $C = 3500 + 2100$ .

STEP 10

Adding those together, we get $C = 5600$ .
So the total cost to transport 12 tons of sugar is $\$5600$ .

STEP 11

Equation: $C = 3500 + 175 \cdot S$
Total cost to transport 12 tons of sugar: $\$5600$

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Studdy Solution

STEP 1

STEP 2

1. Define the variables and their units.
2. Create the cost equation.
3. Calculate the cost for 12 tons.

STEP 3

Let's define what our variables represent. $C$ is the total cost in $\$$ , and $S$ is the amount of sugar transported in tons.

STEP 4

The total cost $C$ has two parts: the fixed cost of renting the trucks, which is $\$3500$ , and the variable cost, which depends on the amount of sugar $S$ .

STEP 5

The variable cost is $\$175$ per ton of sugar.
So, for $S$ tons of sugar, the variable cost is $175 \cdot S$ .

STEP 6

To get the total cost $C$ , we add the fixed cost and the variable cost: $C = 3500 + 175 \cdot S$ .
There's our equation!

STEP 7

Now, we want to find the total cost to transport 12 tons of sugar.
So, we'll substitute $S = 12$ into our equation: $C = 3500 + 175 \cdot 12$ .

STEP 8

Let's calculate that! $175 \cdot 12 = 2100$ .

STEP 9

So, $C = 3500 + 2100$ .

STEP 10

Adding those together, we get $C = 5600$ .
So the total cost to transport 12 tons of sugar is $\$5600$ .

STEP 11

Equation: $C = 3500 + 175 \cdot S$
Total cost to transport 12 tons of sugar: $\$5600$

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Studdy Solution

STEP 1

STEP 2

1. Define the variables and their units.2. Create the cost equation.3. Calculate the cost for 12 tons.

STEP 3

Let's **define** what our variables represent. CCC is the **total cost** in $\$$, and SSS is the **amount of sugar** transported in **tons**.

STEP 4

The **total cost** CCC has two parts: the **fixed cost** of renting the trucks, which is $3500\$3500$3500, and the **variable cost**, which depends on the amount of sugar SSS.

STEP 5

The **variable cost** is $175\$175$175 *per* **ton** of sugar.So, for SSS tons of sugar, the variable cost is 175⋅S175 \cdot S175⋅S.

STEP 6

To get the **total cost** CCC, we **add** the **fixed cost** and the **variable cost**: C=3500+175⋅SC = 3500 + 175 \cdot SC=3500+175⋅S.There's our equation!

STEP 7

Now, we want to find the **total cost** to transport **12 tons** of sugar.So, we'll **substitute** S=12S = 12S=12 into our equation: C=3500+175⋅12C = 3500 + 175 \cdot 12C=3500+175⋅12.

STEP 8

Let's **calculate** that! 175⋅12=2100175 \cdot 12 = 2100175⋅12=2100.

STEP 9

So, C=3500+2100C = 3500 + 2100C=3500+2100.

STEP 10

Adding those together, we get C=5600C = 5600C=5600.So the **total cost** to transport **12 tons** of sugar is $5600\$5600$5600.

STEP 11

Equation: C=3500+175⋅SC = 3500 + 175 \cdot SC=3500+175⋅STotal cost to transport 12 tons of sugar: $5600\$5600$5600

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1. Define the variables and their units.
2. Create the cost equation.
3. Calculate the cost for 12 tons.

Let's define what our variables represent. $C$ is the total cost in $\$$ , and $S$ is the amount of sugar transported in tons.

The total cost $C$ has two parts: the fixed cost of renting the trucks, which is $\$3500$ , and the variable cost, which depends on the amount of sugar $S$ .

The variable cost is $\$175$ per ton of sugar.
So, for $S$ tons of sugar, the variable cost is $175 \cdot S$ .

To get the total cost $C$ , we add the fixed cost and the variable cost: $C = 3500 + 175 \cdot S$ .
There's our equation!

Now, we want to find the total cost to transport 12 tons of sugar.
So, we'll substitute $S = 12$ into our equation: $C = 3500 + 175 \cdot 12$ .

Let's calculate that! $175 \cdot 12 = 2100$ .

So, $C = 3500 + 2100$ .

Adding those together, we get $C = 5600$ .
So the total cost to transport 12 tons of sugar is $\$5600$ .

Equation: $C = 3500 + 175 \cdot S$
Total cost to transport 12 tons of sugar: $\$5600$