2) The earnings for a delivery driver are given by E=15+2d dollars, where d is the distance driven in kilometres. The cost for the driver to travel d kilometres is given by C= 0.3d + 22 dollars. How many kilometres would the delivery driver need to drive to break even?  

To find the number of kilometers the delivery driver would need to drive to break even, we set the earnings $ E $ equal to the cost $ C $.

### Given equations:
- Earnings: $ E = 15 + 2d $
- Cost: $ C = 0.3d + 22 $

To break even, the earnings must equal the cost:

\[
15 + 2d = 0.3d + 22
\]

### Steps to solve:

1. Subtract $ 0.3d $ from both sides to isolate $ d $ on one side:

\[
15 + 2d - 0.3d = 22
\]

\[
15 + 1.7d = 22
\]

2. Subtract 15 from both sides:

\[
1.7d = 22 - 15
\]

\[
1.7d = 7
\]

3. Solve for $ d $:

\[
d = \frac{7}{1.7}
\]

\[
d = 4.12 \, \text{km}
\]

### Conclusion:
The delivery driver needs to drive approximately **4.12 kilometers** to break even.

---

Do you want more details, or have any questions?

Here are 5 follow-up questions for further exploration:

1. What would the driver's earnings be if they drove 10 kilometers?
2. How much would the cost be if the driver drove 10 kilometers?
3. How many kilometers would the driver need to drive to earn a profit of $10?
4. What is the relationship between distance and earnings for the driver?
5. At what distance would the driver's earnings exceed their costs by $5?

**Tip:** When solving break-even problems, set earnings equal to costs and solve for the variable in question.

The earnings for a delivery driver are given by E=15+2d dollars, where d is the distance driven in kilometres. The cost for the driver to travel d kilometres is given by C= 0.3d + 22 dollars. How many kilometres would the delivery driver need to drive to break even?

Find out how to determine the break-even point for a delivery driver whose earnings and costs are represented by linear equations. This problem involves solving linear equations and performing a break-even analysis, making it ideal for students in Grades 9-10. Learn how to calculate the distance at which the driver breaks even with step-by-step solutions.

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