https://r2.erweima.ai/mathbot/image/1725237151460k0g4kuux.jpg

Let's solve the problem step-by-step.

### Problem Analysis:
1. **Part a)** We are given that the number of wagons in train A is to the number of wagons in train B as 5 is to 11, with a total of 80 wagons.

   Let:
   - \( x \) be the common factor for the ratio.
   - Wagons in train A: \( 5x \).
   - Wagons in train B: \( 11x \).

   From the total number of wagons:
   \[
   5x + 11x = 80.
   \]
   Solving this equation gives:
   \[
   16x = 80 \implies x = 5.
   \]
   
   Therefore:
   - Wagons in train A: \( 5 \times 5 = 25 \).
   - Wagons in train B: \( 11 \times 5 = 55 \).

   **Answer for a)**: Train B has more wagons, and the difference is \( 55 - 25 = 30 \).

2. **Part b)** It is estimated that the maintenance cost of each train wagon is 575 soles. We need to find the cost of maintaining train A and 80% of the cost for train B.

   - Maintenance cost for train A:
     \[
     25 \times 575 = 14375 \text{ soles}.
     \]

   - Maintenance cost for train B:
     \[
     55 \times 575 = 31625 \text{ soles}.
     \]

   - 80% of the cost for train B:
     \[
     0.8 \times 31625 = 25300 \text{ soles}.
     \]

   **Answer for b)**: The total cost for maintaining train A and 80% of train B is \( 14375 + 25300 = 39675 \text{ soles}. \)

Would you like further details on this solution, or do you have any other questions?

### Related Questions:
1. How do you calculate the ratio of wagons if the total number was different?
2. What would the costs be if the maintenance cost per wagon changed to 600 soles?
3. How would the ratio change if train A had twice the wagons of train B?
4. How do you determine the percentage difference in costs between train A and train B?
5. What would be the maintenance cost for a fleet of 3 trains with similar ratios?

**Tip:** When dealing with ratios and proportions, always simplify them as much as possible to make calculations easier!

Learn how to solve a ratios and proportions problem involving train wagon numbers and maintenance costs. This problem covers calculating ratios, determining maintenance costs based on given ratios, and applying percentages in mathematical scenarios. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation