Answered

Anna is trying to save some money on her electric bill. Her electric company has come up with a new plan designed to charge customers based on when they use electricity. She is trying to decide if the new interval use plan would be better than the standard use plan for her needs. Calculate the monthly costs of both plans if she uses $1,185\text{ kWh}$ of electricity per month with 500 kWh on-peak usage and the rest off-peak usage.




Standard Use Plan		Interval Use Plan


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8.5 cents/kWh for the first 600 kWh

11 cents/kWh for anything over 600 kWh
&


On-peak hours - 16 cents/kWh

Off-peak hours - 4 cents/kWh
\\

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Astandard use plan - $64.35; interval use plan - $80.00
Bstandard use plan - $115.35; interval use plan - $107.40
Cstandard use plan - $64.35; interval use plan - $107.40
Dstandard use plan - $115.35; interval use plan - $80.00

Verified Answer :

  • Calculate total usage for the Standard Plan by separating the usage into two brackets: \(600 \text{ kWh}\) at 8.5 cents and \(585 \text{ kWh}\) at 11 cents, totaling \(\$115.35\).
  • Calculate total usage for the Interval Plan based on on-peak (\(500 \text{ kWh}\) at 16 cents) and off-peak (\(685 \text{ kWh}\) at 4 cents) hours, totaling \(\$107.40\).
  • Compare the results (\(\$115.35\) and \(\$107.40\)) with the provided options.
  • The correct choice is \(\boxed{\text{b}}\).

Explanation

  1. Analysis of Electricity Usage Data

To determine the monthly cost for each electricity plan, we start by organizing the provided usage data:

  • Total monthly usage: \(1,185 \text{ kWh}\)
  • On-peak usage: \(500 \text{ kWh}\)
  • Off-peak usage = Total usage - On-peak usage = \(1,185 \text{ kWh} - 500 \text{ kWh} = 685 \text{ kWh}\)

These figures will be applied to the rate structures of both the Standard Use Plan and the Interval Use Plan to calculate the final monthly costs.

  1. Calculating the Standard Use Plan Cost

The Standard Use Plan charges 8.5 cents/kWh for the first \(600 \text{ kWh}\) and 11 cents/kWh for usage exceeding this amount.

  • Cost for the first \(600 \text{ kWh}\): \(600 \text{ kWh} \times 8.5 \text{ cents/kWh} = 5,100 \text{ cents}\)
  • Remaining usage: \(1,185 \text{ kWh} - 600 \text{ kWh} = 585 \text{ kWh}\)
  • Cost for the remaining usage: \(585 \text{ kWh} \times 11 \text{ cents/kWh} = 6,435 \text{ cents}\)
  • Total cost in cents: \(5,100 \text{ cents} + 6,435 \text{ cents} = 11,535 \text{ cents}\)
  • Converting to dollars: \(11,535 \text{ cents} \div 100 = \$115.35\)

Thus, the monthly cost for the Standard Use Plan is \(\$115.35\).

  1. Calculating the Interval Use Plan Cost and Final Comparison

The Interval Use Plan charges 16 cents/kWh for on-peak usage and 4 cents/kWh for off-peak usage.

  • Cost for on-peak usage: \(500 \text{ kWh} \times 16 \text{ cents/kWh} = 8,000 \text{ cents}\)
  • Cost for off-peak usage: \(685 \text{ kWh} \times 4 \text{ cents/kWh} = 2,740 \text{ cents}\)
  • Total cost in cents: \(8,000 \text{ cents} + 2,740 \text{ cents} = 10,740 \text{ cents}\)
  • Converting to dollars: \(10,740 \text{ cents} \div 100 = \$107.40\)

Thus, the monthly cost for the Interval Use Plan is \(\$107.40\). Comparing our calculated values (\(\$115.35\) for the Standard plan and \(\$107.40\) for the Interval plan) with the given options, we identify that the correct choice is b.

Examples

Calculating electricity bills based on usage plans is a practical application of basic arithmetic and weighted averages. For example, if you are a small business owner, understanding whether a time-of-use (TOE) tariff is more cost-effective than a flat rate allows you to schedule high-energy tasks—like running heavy machinery or heating ovens—during lower-cost, off-peak periods, directly impacting your bottom line and operational efficiency.