An office building has three air conditioning units, one for each office. Each unit runs only when employees are working. The tables below show the number of hours employees worked at each office over a three-month period and the total air conditioning electric costs for the entire office for each month.

Number of Hours Worked

| | Unit A | Unit B | Unit C |
|---------|--------|--------|--------|
| June | 184 | 207 | 276 |
| July | 174 | 198 | 264 |
| August | 168 | 189 | 242 |

Total Air Conditioning Electric Costs

| | Cost |
|---------|-----------|
| June | [tex]$142.60 |
| July | $[/tex]135.96 |
| August | $128.30 |

How much does it cost to run Unit A per hour?

To calculate the cost to run Unit A per hour, let's break down the problem into a series of steps:

### Step 1: Calculate the Total Hours Worked by Each Unit Over the Three Months

For Unit A:
- June: 184 hours
- July: 174 hours
- August: 168 hours
- Total Hours for Unit A:
[tex]$ 184 + 174 + 168 = 526 $[/tex] hours

For Unit B:
- June: 207 hours
- July: 198 hours
- August: 189 hours
- Total Hours for Unit B:
[tex]$ 207 + 198 + 189 = 594 $[/tex] hours

For Unit C:
- June: 276 hours
- July: 264 hours
- August: 242 hours
- Total Hours for Unit C:
[tex]$ 276 + 264 + 242 = 782 $[/tex] hours

### Step 2: Calculate the Total Hours Worked by All Units Over the Three Months

Total Hours for All Units:
[tex]\[ 526 \text{ (Unit A)} + 594 \text{ (Unit B)} + 782 \text{ (Unit C)} = 1902 \][/tex] hours

### Step 3: Calculate the Total Cost Over the Three Months

Total Cost for All Units:
- June: \[tex]$142.60 - July: \$[/tex]135.96
- August: \[tex]$128.30 - Total Cost: $ 142.60 + 135.96 + 128.30 = 406.86 $ dollars ### Step 4: Calculate the Cost per Hour for All Units Cost per Hour for All Units: \[ \frac{\text{Total Cost}}{\text{Total Hours}} = \frac{406.86 \text{ dollars}}{1902 \text{ hours}} \approx 0.2139 \text{ dollars per hour} \] ### Step 5: Calculate the Cost Attributed to Unit A Using the cost per hour for all units combined, \[ \text{Total Cost for Unit A} = \text{Cost per Hour} \times \text{Total Hours for Unit A} \] \[ \text{Total Cost for Unit A} = 0.2139 \times 526 \approx 112.54 \text{ dollars} \] Now, to find the cost per hour for Unit A, ### Step 6: Calculate the Cost per Hour for Unit A \[ \text{Cost per Hour for Unit A} = \frac{\text{Total Cost for Unit A}}{\text{Total Hours for Unit A}} \] \[ \text{Cost per Hour for Unit A} = \frac{112.54 \text{ dollars}}{526 \text{ hours}} \approx 0.2139 \text{ dollars per hour} \] So, the cost to run Unit A per hour is approximately \$[/tex]0.2139.