Aes of Linear ations A truck rental company rents a moving truck for one day by charging $$ \$ 24 $$ plus $$ \$ 0.12 $$ per mile. Write a linear equation that relates the cost C , in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 200 miles? 489 miles? Type the linear equation that relates the cost C , in dollars, of renting the truck to the number of x miles driven. $$ 24.05 \%, 6.01 $$ of 25 points $$ \mathrm{C}=24+0.12 \mathrm{x} $$ (Use integers or decimals for any numbers in the expression. Do not include the $$ \$ $$ symbol in your answer.) What is the cost of renting the truck if the truck is driven 200 miles? $$ \mathrm{C}=\$ \square $$

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UpStudy AI · Accepted Answer

To solve the problem, we will follow these steps:

1. **Identify the linear equation** that relates the cost $$ C $$ to the number of miles driven $$ x $$.
2. **Calculate the cost** for driving 200 miles and 489 miles using the linear equation.

### Step 1: Write the Linear Equation

The cost $$ C $$ of renting the truck consists of a fixed fee of $$ 24 $$ dollars plus a variable cost of $$ 0.12 $$ dollars per mile driven. Therefore, the linear equation can be expressed as:

$$
C = 24 + 0.12x
$$

### Step 2: Calculate the Cost for 200 Miles

Now, we will substitute $$ x = 200 $$ into the equation to find the cost:

$$
C = 24 + 0.12 \cdot 200
$$

Calculating the variable cost:

$$
0.12 \cdot 200 = 24
$$

Now, substituting back into the equation:

$$
C = 24 + 24 = 48
$$

So, the cost of renting the truck if it is driven 200 miles is:

$$
C = 48
$$

### Step 3: Calculate the Cost for 489 Miles

Next, we will substitute $$ x = 489 $$ into the equation:

$$
C = 24 + 0.12 \cdot 489
$$

Calculating the variable cost:

$$
0.12 \cdot 489 = 58.68
$$

Now, substituting back into the equation:

$$
C = 24 + 58.68 = 82.68
$$

So, the cost of renting the truck if it is driven 489 miles is:

$$
C = 82.68
$$

### Final Answers

1. The linear equation is:
   $$
   C = 24 + 0.12x
   $$

2. The cost of renting the truck if driven 200 miles is:
   $$
   C = 48
   $$

3. The cost of renting the truck if driven 489 miles is:
   $$
   C = 82.68
   $$
The linear equation is $$ C = 24 + 0.12x $$. If the truck is driven 200 miles, the cost is \$48. If the truck is driven 489 miles, the cost is \$82.68.

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