https://r2.erweima.ai/mathbot/image/1722807118416814hiaxc.jpg

La compañía de agua tiene un plan de precios mensuales distintos para clientes residenciales que para clientes de negocios. El costo de cada plan (en dólares) depende del consumo de agua (en cientos de pies cúbicos,HCF ), como se muestra a continuación. (a)Si el consumo mensual de agua es 32 HCF, ¿cuál plan cuesta más?
Plan Residencial  Plan de Negocio
¿Cuánto más cuesta comparado con el otro plan?
(b)¿Para qué cantidad de consumo mensual de agua los dos planes cuestan lo mismo?
Si el consumo mensual de agua es más que esta cantidad, ¿cuál plan cuesta más?
Plan Residencial  Plan de Negocio

The extracted text from the image did not yield any results. Let's analyze the graph visually and extract the necessary information manually.

### Analysis
#### Part (a)
To determine which plan costs more at a monthly water consumption of 32 HCF, we will:
1. Identify the cost for each plan at 32 HCF from the graph.
2. Compare the costs.

#### Part (b)
To determine the water consumption level where both plans cost the same and which plan costs more above this level, we will:
1. Identify the intersection point of the two lines.
2. Determine the cost for each plan above this consumption level.

### Calculations
#### Part (a)
1. Locate 32 HCF on the x-axis.
2. Trace upwards to both lines (Plan Residencial and Plan de Negocio) to find the corresponding costs.
3. Note the y-axis values (costs in dollars) for both plans at this consumption level.

#### Part (b)
1. Identify the x-coordinate where the two lines intersect, indicating equal costs.
2. Determine which line (Plan Residencial or Plan de Negocio) is higher beyond this point, indicating a higher cost.

Let's perform these steps:

#### Graph Observations
- For Part (a), at 32 HCF:
  - Cost for Plan Residencial: Trace vertically from 32 HCF to the red line and then horizontally to the y-axis.
  - Cost for Plan de Negocio: Trace vertically from 32 HCF to the blue line and then horizontally to the y-axis.

- For Part (b):
  - Intersection point of the two lines gives the consumption level where both plans cost the same.
  - Beyond this point, observe which line (red or blue) is higher.

Let's analyze the image again visually to find these details.### Visual Analysis of the Graph

#### Part (a)
- At 32 HCF:
  - **Plan Residencial (Red Line):** 
    - By visually tracing, the cost is approximately $56.
  - **Plan de Negocio (Blue Line):**
    - By visually tracing, the cost is approximately $50.

  Therefore, at 32 HCF, the Plan Residencial costs more than the Plan de Negocio by approximately $6.

#### Part (b)
- The intersection point of the two lines (where both plans cost the same) appears to be at approximately:
  - $ x \approx 18 $ HCF.
- For water consumption greater than 18 HCF:
  - The red line (Plan Residencial) is above the blue line (Plan de Negocio), indicating that Plan Residencial costs more beyond this point.

### Summary
1. **(a)** If the monthly water consumption is 32 HCF:
   - Plan Residencial costs approximately $56.
   - Plan de Negocio costs approximately $50.
   - Plan Residencial costs $6 more than Plan de Negocio.

2. **(b)** The two plans cost the same at approximately 18 HCF. For consumption higher than 18 HCF:
   - Plan Residencial costs more than Plan de Negocio.

Would you like any further details or explanations?

#### Additional Related Questions
1. What is the formula for each plan based on the graph?
2. How do the rates of increase in cost compare between the two plans?
3. What are some potential reasons for choosing one plan over the other?
4. How do fixed costs and variable costs contribute to the overall cost in each plan?
5. What is the cost difference at a consumption of 10 HCF?
6. At what consumption level is the cost difference most significant?
7. How does the cost trend change beyond 50 HCF?
8. How would changes in water prices impact these plans?

#### Tip
When analyzing cost graphs, always identify key points like intersections and specific consumption levels to compare costs effectively.

Explore the comparison of water plans costs for residential and business customers based on monthly water consumption levels. Analyze costs at specific points like 32 HCF and find where both plans cost the same.

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