https://file.aiquickdraw.com/mathbot/file/1729469581927a7h7cin8.jpg

Let's analyze the image step by step. The problem provides the function $ C(x) = 1.5x + 95 $, where $ C(x) $ represents the cost (in dollars) of towing a car, and $ x $ represents the number of miles towed.

We will solve each part:

### (a) What is the cost of towing a car 30 miles?
The formula is $ C(x) = 1.5x + 95 $. To find the cost for 30 miles, substitute $ x = 30 $:
\[
C(30) = 1.5(30) + 95 = 45 + 95 = 140.
\]
So, the cost is **$140**.

### (b) If the cost of towing a car is $194, how many miles was it towed?
We are given $ C(x) = 194 $ and need to find $ x $. Set the equation:
\[
194 = 1.5x + 95.
\]
Subtract 95 from both sides:
\[
99 = 1.5x.
\]
Now, divide by 1.5:
\[
x = \frac{99}{1.5} = 66.
\]
The car was towed **66 miles**.

### (c) Suppose that you have only $128. What is the maximum number of miles that you can be towed?
Set $ C(x) = 128 $ and solve for $ x $:
\[
128 = 1.5x + 95.
\]
Subtract 95 from both sides:
\[
33 = 1.5x.
\]
Now, divide by 1.5:
\[
x = \frac{33}{1.5} = 22.
\]
So, you can be towed a maximum of **22 miles**.

### (d) What is the domain of $ C(x) $?
Since $ x $ represents the number of miles towed, and this number must be non-negative, the domain is:
\[
\text{Domain: } x \geq 0.
\]

---

Do you need any further details or explanations? Here are five related questions to deepen your understanding:

1. What would be the cost to tow a car for 100 miles?
2. If the towing cost is $250, how far was the car towed?
3. How would the function change if the base fee increased to $120?
4. If you can spend up to $500, what is the maximum distance the car can be towed?
5. What happens to the function if the price per mile increases to $2?

**Tip:** Always check the units in word problems. Here, the cost is in dollars and the distance in miles—keeping track of these units helps avoid errors.

The cost C, in dollars, to tow a car is modeled by the function C(x) = 1.5x + 95, where x is the number of miles towed.
(a) What is the cost of towing a car 30 miles?
(b) If the cost of towing a car is $194, how many miles was it towed?
(c) Suppose that you have only $128. What is the maximum number of miles that you can be towed?
(d) What is the domain of C?

Learn how to solve real-world problems involving towing costs with the linear equation C(x) = 1.5x + 95. This problem involves determining the cost of towing a car over different distances and solving for the number of miles based on cost. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation