Answered

Shanika and Vanesa are comparing their electric bills for the past month. Shanika is on a standard use plan, while Vanesa is on an interval use plan. Each person's usage is listed on the chart below:




Standard Use Plan		Interval Use Plan


\begin{tabular}[t]{l}
7.5 cents/kWh for the first 400 kWh

10 cents/kWh for the next 400 kWh

12.5 cents/kWh for anything over 800 kWh
&


On-peak hours - 15 cents/kWh

Off-peak hours - 3 cents/kWh
\\

\hline

\end{tabular}



Both women use 1,325 kWh for the given 30-day period. Vanesa uses 500 kWh during on-peak hours and 825 kWh during off-peak hours. Which person ends up paying more for their utilities? How much more?


AVanesa pays \$35.88 more than Shanika.
BVanesa pays \$99.75 more than Shanika.
CShanika pays \$35.88 more than Vanesa.
DShanika pays \$99.75 more than Vanesa.

Verified Answer :

  • Calculate Shanika's total cost using tiered pricing: \(\$30.00 + \$40.00 + \$65.625 = \$135.625\).
  • Calculate Vanesa's total cost using peak/off-peak pricing: \(\$75.00 + \$24.75 = \$99.75\).
  • Find the difference by subtracting the costs: \(\$135.625 - \$99.75 = \$35.875\).
  • Identify that Shanika pays more, with the rounded difference being \(\$35.88\), matching option \(\boxed{\text{c}}\).

Explanation

  1. Calculate Shanika's Utility Cost

To determine who pays more for their electricity, we need to calculate the total cost for both Shanika and Vanesa based on their respective usage plans.

For Shanika (Standard Use Plan), the total usage is 1,325 kWh. The costs are tiered:

  • First 400 kWh at 7.5 cents/kWh (\(\$0.075\)/kWh): \(400 \times 0.075 = \$30.00\).
  • Next 400 kWh at 10 cents/kWh (\(\$0.10\)/kWh): \(400 \times 0.10 = \$40.00\).
  • Remaining kWh above 800 kWh (\(1,325 - 800 = 525\) kWh) at 12.5 cents/kWh (\(\$0.125\)/kWh): \(525 \times 0.125 = \$65.625\).

Adding these together, Shanika's total cost is \(\$30.00 + \$40.00 + \$65.625 = \$135.625\).

  1. Calculate Vanesa's Utility Cost

For Vanesa (Interval Use Plan), the total usage is 1,325 kWh, broken down as:

  • On-peak hours: 500 kWh at 15 cents/kWh (\(\$0.15\)/kWh): \(500 \times 0.15 = \$75.00\).
  • Off-peak hours: 825 kWh at 3 cents/kWh (\(\$0.03\)/kWh): \(825 \times 0.03 = \$24.75\).

Adding these together, Vanesa's total cost is \(\$75.00 + \$24.75 = \$99.75\).

  1. Compare Costs and Determine the Difference

Now, we compare the total costs to determine the difference:

  • Shanika's cost: \(\$135.625\)
  • Vanesa's cost: \(\$99.75\)

Since \(\$135.625 > \$99.75\), Shanika pays more. The difference is \(\$135.625 - \$99.75 = \$35.875\). Rounding this to the nearest cent, we get \(\$35.88\). Therefore, Shanika pays \(\$35.88\) more than Vanesa, which corresponds to option c. The final answer is \(\boxed{\text{c}}\).

Examples

Utility companies often provide different pricing models, such as tiered or time-of-use plans, to encourage conservation during high-demand hours. By calculating your bill using these models, you can make informed decisions about your energy habits. For example, by shifting heavy power usage—like running a dishwasher or laundry machine—to off-peak hours, you can significantly reduce your monthly costs, just as Vanesa has done in this comparison. Understanding how these rates apply to your total usage is a practical way to manage household finances effectively.

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