A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes.
 
Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times, for a total distance traveled of 141 miles.
This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times, for a total distance traveled of 123.75 miles.

What is the distance of the morning route in miles?
A.5.25 miles

We can set up a system of equations to find the distance of the morning route.

Let:
- \( x \) be the distance of the morning route (in miles).
- \( y \) be the distance of the afternoon route (in miles).

We are given two pieces of information for each month.

### Last month:
- 16 times on the morning route and 12 times on the afternoon route, for a total of 141 miles.
This gives us the equation:
\[
16x + 12y = 141
\]

### This month:
- 10 times on the morning route and 15 times on the afternoon route, for a total of 123.75 miles.
This gives us the second equation:
\[
10x + 15y = 123.75
\]

### Solving the system of equations:
We will solve this system by elimination or substitution. Let’s use elimination.

First, we multiply both equations to align the coefficients for one of the variables (let’s eliminate \( y \)).

Multiply the first equation by 5 and the second by 4:
\[
5(16x + 12y) = 5(141) \quad \Rightarrow \quad 80x + 60y = 705
\]
\[
4(10x + 15y) = 4(123.75) \quad \Rightarrow \quad 40x + 60y = 495
\]

Now subtract the second equation from the first:
\[
(80x + 60y) - (40x + 60y) = 705 - 495
\]
\[
40x = 210
\]
\[
x = \frac{210}{40} = 5.25
\]

So, the distance of the morning route is **5.25 miles**.

The correct answer is **A. 5.25 miles**.

Would you like a further breakdown of the steps or details on any part of the solution?

Here are some related questions to explore:
1. What is the distance of the afternoon route?
2. How can you check if both equations are consistent with the result?
3. What would happen if the number of routes increased for each month but with the same distances?
4. What are other methods to solve this system of equations?
5. How does the concept of linear equations apply to real-life scenarios like this?

**Tip**: When solving systems of equations, elimination works well when you can easily align coefficients by multiplication!

A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes. Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times, for a total distance traveled of 141 miles. This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times, for a total distance traveled of 123.75 miles. What is the distance of the morning route in miles? A.5.25 miles

Learn how to solve a real-world system of equations problem involving a mail carrier's delivery routes. Last month, the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times, traveling a total of 141 miles. This month, the carrier delivered on the morning route 10 times and the afternoon route 15 times, traveling a total of 123.75 miles. Find the distance of the morning route using algebraic methods. Suitable for students in Grades 8-10.

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