Final answer:
The problem requires solving for the number of kWh at which the cost under a new utility deal equals the cost under the previous billing arrangement.
Given the flat rate of the new deal and the fact that the fixed service charge is no longer applied, it's likely the Antonios used closest to 400 kWh for their monthly bill to be the same under both plans.
Step-by-step explanation:
The problem involves finding the number of kWh the Antonios used that resulted in the same charge under the new deal as with their regular Period 1 charge. Under the new deal, the cost is $0.09 per kWh. To find the usage that results in the same charge for both plans, we need to set the new deal cost equal to the cost under the regular Period 1 tariff and solve for kWh.
Let's suppose the regular Period 1 charge is made up of $0.12 per kWh plus a fixed service charge. Since we are not given the fixed service charge, we use the cost of the electricity company's new deal ($45 for 500 kWh) as an example to estimate the Antonios' usage.
If the Antonios pay $45 under the new deal, at a rate of $0.09 per kWh, the amount of energy they used would be calculated by:
$45 = $0.09 × number of kWh
number of kWh = $45 / $0.09 per kWh
number of kWh = 500 kWh
However, the Antonios' actual charge with the regular Period 1 charge has to also equate to $45. As this includes both the consumption cost and the fixed service charge, the actual kWh they consumed would have to be lower than 500 kWh to account for the service charge addition.
Among the options provided (A) 500 kWh, (B) 400 kWh, (C) 600 kWh, (D) 550 kWh, it's plausible that the closest value would be (B) 400 kWh. Since option (A) 500 kWh would equal $45 just on consumption under the new plan, and higher usage would result in a higher bill, the only feasible choice closest to the regular bill of $45 would be the lower usage estimate of 400 kWh.