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Isaiah is trying to decide if the interval use plan is better than the standard use plan for his electricity consumption. Calculate the monthly costs of both plans if he uses 1,275 kWh of electricity per month with 515 kWh on-peak usage and the rest off-peak usage.




Standard Use Plan		Interval Use Plan

7.5 cents/kWh for the first 400 kWh		On-peak hours - 15 cents/kWh

10 cents/kWh for anything over 400 kWh		Off-peak hours - 3 cents/kWh





Astandard use plan - \$117.50; interval use plan - \$107.25
Bstandard use plan - \$87.50; interval use plan - \$86.25
Cstandard use plan - \$117.50; interval use plan - \$86.25
Dstandard use plan - \$87.50; interval use plan - \$107.25

Verified Answer :

  • Determine the total off-peak electricity usage by subtracting on-peak usage from the total: \(1{,}275 - 515 = 760\) kWh.
  • Calculate the Standard Use Plan cost by applying the tier-based pricing: \((400 \times 0.075) + (875 \times 0.10) = \$117.50\).
  • Calculate the Interval Use Plan cost by applying the time-based pricing: \((515 \times 0.15) + (760 \times 0.03) = \$100.05\).
  • The calculated monthly costs are \(\boxed{\text{standard use plan - \$117.50; interval use plan - \$100.05}}\).

Explanation

  1. Analyzing Electricity Usage

To determine the monthly electricity costs for both plans, we first identify the electricity usage patterns. Isaiah consumes a total of \(1{,}275\) kWh. Of this, \(515\) kWh is consumed during on-peak hours. The remaining electricity is used during off-peak hours:
\[\text{Off-peak usage} = 1{,}275 \text{ kWh} - 515 \text{ kWh} = 760 \text{ kWh}.\]

  1. Calculating Standard Use Plan Cost

The Standard Use Plan charges based on total consumption:

  • The first \(400\) kWh are charged at \(7.5\) cents per kWh.
  • The remaining \((1{,}275 - 400) = 875\) kWh are charged at \(10\) cents per kWh.

The total cost in cents is:
\[\text{Cost}_S = (400 \times 7.5) + (875 \times 10) = 3{,}000 + 8{,}750 = 11{,}750 \text{ cents}.\]
Converting to dollars by dividing by \(100\):
\[\text{Cost}_S = \frac{11{,}750}{100} = \$117.50.\]

  1. Calculating Interval Use Plan Cost

The Interval Use Plan charges based on the time of day:

  • On-peak usage of \(515\) kWh is charged at \(15\) cents per kWh.
  • Off-peak usage of \(760\) kWh is charged at \(3\) cents per kWh.

The total cost in cents is:
\[\text{Cost}_I = (515 \times 15) + (760 \times 3) = 7{,}725 + 2{,}280 = 10{,}005 \text{ cents}.\]
Converting to dollars by dividing by \(100\):
\[\text{Cost}_I = \frac{10{,}005}{100} = \$100.05.\]

  1. Conclusion

Comparing the costs calculated with the provided options:

  • The Standard Use Plan cost is \(\$117.50\).
  • The Interval Use Plan cost is \(\$100.05\).

Given the structure of the question, there may be a discrepancy in the options provided for the Interval Use Plan. However, based strictly on the data provided, the calculated costs are \(\$117.50\) and \(\$100.05\). Given the similarity to option (a), we conclude the standard plan is \(\$117.50\) and the interval plan calculation based on the usage given is \(\$100.05\), noting the calculation procedure is consistent with the standard business model.
The final costs are \(\boxed{\text{standard use plan - \$117.50; interval use plan - \$100.05}}\).

Examples

Understanding electricity billing plans is a vital real-life skill for household budgeting. By analyzing peak vs. off-peak rates, consumers can make informed decisions to shift heavy energy tasks (like running a dryer or dishwasher) to off-peak hours to save money. For example, if a homeowner learns that their local utility company offers a significantly lower rate for off-peak usage, they might program their smart appliances to run late at night, ultimately reducing their monthly utility expenses.

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