Question

2. An agency rents car for one day and charges 1000 birr plus 50 cents per kilo Meter the car is driven.
a) Write the equation for one day’s rental (y) in terms of the number of Kilo Meters driven (x)
b) Interpret the slope and the y- intercept
c) What is the renter’s cost per mile if a car is driven 100 kilo meters? 200 Kilo Meters?

Answer 1

Let's tackle each part of your question step by step.

### a) Write the equation for one day’s rental (y) in terms of the number of kilometers driven (x).

The cost consists of a fixed rental charge plus a variable charge based on the kilometers driven. The fixed rental charge is 1000 birr, and the variable charge is 0.50 birr (50 cents) for each kilometer driven.

Thus, the equation can be formulated as:

\[
y = 1000 + 0.50x
\]

where:
- \( y \) is the total cost in birr,
- \( x \) is the number of kilometers driven.

### b) Interpret the slope and the y-intercept.

In the equation \( y = 1000 + 0.50x \):

- **Y-intercept**: The y-intercept is the value of \( y \) when \( x = 0 \). Here, when no kilometers are driven (\( x = 0 \)), the cost is \( y = 1000 \) birr. This represents the fixed rental charge for one day, regardless of usage.

- **Slope**: The slope of the equation is the coefficient of \( x \), which is 0.50. This indicates that for every additional kilometer driven, the total cost increases by 0.50 birr. In other words, the cost per kilometer driven is 0.50 birr.

### c) What is the renter’s cost per mile if a car is driven 100 kilometers? 200 kilometers?

To calculate the total cost for driving 100 and 200 kilometers, substitute these values into the equation.

1. **For 100 kilometers**:

\[
y = 1000 + 0.50(100) = 1000 + 50 = 1050 \text{ birr}
\]

2. **For 200 kilometers**:

\[
y = 1000 + 0.50(200) = 1000 + 100 = 1100 \text{ birr}
\]

### Summary of the costs:
- **Cost for 100 kilometers**: 1050 birr
- **Cost for 200 kilometers**: 1100 birr

### Cost per mile:
To find the cost per mile for driving 100 kilometers and 200 kilometers, we first need to convert kilometers to miles. There are approximately 0.621371 miles in a kilometer.

- **100 kilometers in miles**:
\[
100 \text{ km} \times 0.621371 = 62.1371 \text{ miles}
\]
Cost per mile:
\[
\text{Cost per mile} = \frac{1050 \text{ birr}}{62.1371 \text{ miles}} \approx 16.9 \text{ birr/mile}
\]

- **200 kilometers in miles**:
\[
200 \text{ km} \times 0.621371 = 124.2742 \text{ miles}
\]
Cost per mile:
\[
\text{Cost per mile} = \frac{1100 \text{ birr}}{124.2742 \text{ miles}} \approx 8.85 \text{ birr/mile}
\]

### Final Costs per mile:
- **Cost per mile driving 100 kilometers**: approximately 16.9 birr/mile
- **Cost per mile driving 200 kilometers**: approximately 8.85 birr/mile