Sure, let’s break down the problem step by step.
### Baum Family's Bill:
The Baum family is on a standard use plan with the following rates:
- 8.5 cents/kWh for the first 400 kWh
- 12 cents/kWh for the next 400 kWh
- 14.5 cents/kWh for anything over 800 kWh
The total usage for the Baum family is 1250 kWh.
1. First 400 kWh:
[tex]\[ \text{Cost} = 400 \, \text{kWh} \times 8.5 \, \text{cents/kWh} = 3400 \, \text{cents} = \$34.00 \][/tex]
2. Next 400 kWh:
[tex]\[ \text{Cost} = 400 \, \text{kWh} \times 12 \, \text{cents/kWh} = 4800 \, \text{cents} = \$48.00 \][/tex]
3. Remaining 450 kWh (since 1250 - 800 = 450 kWh):
[tex]\[ \text{Cost} = 450 \, \text{kWh} \times 14.5 \, \text{cents/kWh} = 6525 \, \text{cents} = \$65.25 \][/tex]
4. Total cost for the Baum family:
[tex]\[ \text{Total Cost} = 34.00 + 48.00 + 65.25 = \$147.25 \][/tex]
### Freeman Family's Bill:
The Freeman family is on an interval use plan with the following rates:
- 13 cents/kWh during on-peak hours
- 2 cents/kWh during off-peak hours
The usage for the Freeman family is:
- 400 kWh during on-peak hours
- 850 kWh during off-peak hours
1. On-peak hours (400 kWh):
[tex]\[ \text{Cost} = 400 \, \text{kWh} \times 13 \, \text{cents/kWh} = 5200 \, \text{cents} = \$52.00 \][/tex]
2. Off-peak hours (850 kWh):
[tex]\[ \text{Cost} = 850 \, \text{kWh} \times 2 \, \text{cents/kWh} = 1700 \, \text{cents} = \$17.00 \][/tex]
3. Total cost for the Freeman family:
[tex]\[ \text{Total Cost} = 52.00 + 17.00 = \$69.00 \][/tex]
### Comparison:
Now, we compare the total costs:
- Baum family: \[tex]$147.25
- Freeman family: \$[/tex]69.00
The Baum family ends up paying more. The difference in cost is:
[tex]\[ \text{Difference} = 147.25 - 69.00 = \$78.25 \][/tex]
Therefore, the Baum family pays \[tex]$78.25 more than the Freeman family.
### Correct Answer:
d. The Baum family pays \$[/tex]78.25 more than the Freeman family.
