The Baum and the Freeman families are comparing their electric bills for the past month. The Baum family is on a standard use plan, and the Freeman family is on an interval use plan. Each family's usage is listed in the chart below:

\begin{tabular}{|c|c|}
\hline
\textbf{Standard Use Plan} & \textbf{Interval Use Plan} \\
\hline
8.5 cents [tex]$/ \text{kWh}$[/tex] for the first 400 kWh & On-peak hours - 13 cents [tex]$/ \text{kWh}$[/tex] \\
12 cents [tex]$/ \text{kWh}$[/tex] for the next 400 kWh & Off-peak hours - 2 cents [tex]$/ \text{kWh}$[/tex] \\
14.5 cents [tex]$/ \text{kWh}$[/tex] for anything over 800 kWh & \\
\hline
\end{tabular}

Both families use 1250 kWh for the given 30-day period. The Freeman family uses 400 kWh during on-peak hours and 850 kWh during off-peak hours. Which family ends up paying more for their utilities? How much more?

a. The Freeman family pays [tex]$\$[/tex]260.83[tex]$ more than the Baum family.

b. The Freeman family pays $[/tex]\[tex]$250.00$[/tex] more than the Baum family.

c. The Baum family pays [tex]$\$[/tex]69.00[tex]$ more than the Freeman family.

d. The Baum family pays $[/tex]\[tex]$78.25$[/tex] more than the Freeman family.

Please select the best answer from the choices provided.



Answer :

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.