A weaver working with a handloom is able to produce 16 yards of fabric per day. The typical weaver is paid £16 for a day's work. A loom powered by a steam engine is able to produce 116 yards of fabric per day. The powered loom still needs a worker to operate it, earning £16 per day, but also needs 16 pounds of coal to power it. At what price per pound of coal does the cost of producing fabric by power loom equal the cost of producing it by handloom? Round your final answer to two decimal places.

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Chapter1: Making Economics Decisions
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### Comparative Production Costs of Handloom and Steam-Powered Loom

**Scenario Description:**
1. **Handloom Production:**
   - A weaver working with a handloom can produce 16 yards of fabric per day.
   - The weaver earns £16 for a day's work.

2. **Steam-Powered Loom Production:**
   - A loom powered by a steam engine can produce 116 yards of fabric per day.
   - This powered loom still requires a worker to operate it, who also earns £16 per day.
   - In addition to the worker's wage, the powered loom requires 16 pounds of coal to run.

**Problem Statement:**
Determine at what price per pound of coal the cost of producing fabric with a steam-powered loom becomes equal to the cost of producing fabric with a handloom. 

**Final Calculation Requirement:**
- Round your final answer to two decimal places.

**Detailed Calculation Steps:**
1. **Cost Calculation for Handloom:**
   - Daily production with handloom: 16 yards
   - Daily wage of weaver: £16
   - Cost per yard of fabric = Total daily wage / Total yards produced per day
   - Cost per yard of fabric by handloom = £16 / 16 yards = £1.00 per yard

2. **Cost Calculation for Steam-Powered Loom:**
   - Daily production with steam-powered loom: 116 yards
   - Daily wage of worker: £16
   - Let the price per pound of coal be \(C\). Total coal cost per day = 16 pounds * \(C\)
   - Total daily cost for steam-powered loom = Wage of worker + Cost of coal = £16 + 16*C
   - Cost per yard of fabric = Total daily cost / Total yards produced per day
   - Cost per yard of fabric by steam-powered loom = (£16 + 16*C) / 116 yards

3. **Equality Condition:**
   - To find the price per pound of coal where the cost per yard of fabric is the same for both methods, set the costs equal to each other: 
   - £1.00 = (£16 + 16*C) / 116
   - Solving for \(C\):

     \[
     116 = 16 + 16C
     \]

     \[
     116 - 16 = 16C
     \]

     \[
Transcribed Image Text:### Comparative Production Costs of Handloom and Steam-Powered Loom **Scenario Description:** 1. **Handloom Production:** - A weaver working with a handloom can produce 16 yards of fabric per day. - The weaver earns £16 for a day's work. 2. **Steam-Powered Loom Production:** - A loom powered by a steam engine can produce 116 yards of fabric per day. - This powered loom still requires a worker to operate it, who also earns £16 per day. - In addition to the worker's wage, the powered loom requires 16 pounds of coal to run. **Problem Statement:** Determine at what price per pound of coal the cost of producing fabric with a steam-powered loom becomes equal to the cost of producing fabric with a handloom. **Final Calculation Requirement:** - Round your final answer to two decimal places. **Detailed Calculation Steps:** 1. **Cost Calculation for Handloom:** - Daily production with handloom: 16 yards - Daily wage of weaver: £16 - Cost per yard of fabric = Total daily wage / Total yards produced per day - Cost per yard of fabric by handloom = £16 / 16 yards = £1.00 per yard 2. **Cost Calculation for Steam-Powered Loom:** - Daily production with steam-powered loom: 116 yards - Daily wage of worker: £16 - Let the price per pound of coal be \(C\). Total coal cost per day = 16 pounds * \(C\) - Total daily cost for steam-powered loom = Wage of worker + Cost of coal = £16 + 16*C - Cost per yard of fabric = Total daily cost / Total yards produced per day - Cost per yard of fabric by steam-powered loom = (£16 + 16*C) / 116 yards 3. **Equality Condition:** - To find the price per pound of coal where the cost per yard of fabric is the same for both methods, set the costs equal to each other: - £1.00 = (£16 + 16*C) / 116 - Solving for \(C\): \[ 116 = 16 + 16C \] \[ 116 - 16 = 16C \] \[
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