Question

The “Limited Plan” offers a 15% discount for power usage between 7:00 p.m. and 9:00 a.m. if most of your usage happens during that time. If not, then you lose your discount and you pay a 20% premium on the usage outside of that time. The cost per kilowatt hour is $0.05432. How much would you have paid in March if you used 450 KWH between 7:00 p.m. and 9:00 a.m. and 465 KWH between 9:00 a.m. and 7:00 p.m.? (1 point) Responses $49.70 $49.70 $51.08 $51.08 $54.75 $54.75 $42.25 $42.25

Answer 1

To calculate the total cost of your energy usage with the “Limited Plan,” let’s break it down into two parts:

1. Calculate the cost of usage between 7:00 p.m. and 9:00 a.m. (450 kWh) with a 15% discount.
2. Calculate the cost of usage between 9:00 a.m. and 7:00 p.m. (465 kWh) with a 20% premium.

Step 1: Calculate the cost of night usage (7:00 p.m. to 9:00 a.m.)

• Normal rate = $0.05432 per kWh
• Discount = 15%
• Discounted rate = Normal rate - (Normal rate × Discount)

\[ \text{Discounted rate} = 0.05432 - (0.05432 \times 0.15) = 0.05432 - 0.008148 = 0.046172 \]

• Cost for night usage:

\[ \text{Cost (Night)} = 450 \text{ kWh} \times 0.046172 = 20.77 \]

Step 2: Calculate the cost of day usage (9:00 a.m. to 7:00 p.m.)

• Premium = 20%
• Premium rate = Normal rate + (Normal rate × Premium)

\[ \text{Premium rate} = 0.05432 + (0.05432 \times 0.20) = 0.05432 + 0.010864 = 0.065184 \]

• Cost for day usage:

\[ \text{Cost (Day)} = 465 \text{ kWh} \times 0.065184 = 30.33 \]

Step 3: Add both costs together:

\[ \text{Total cost} = \text{Cost (Night)} + \text{Cost (Day)} = 20.77 + 30.33 = 51.10 \]

Since we need to find one of the corresponding answers, rounding to suit the options given, it looks like $51.08 is the closest valid choice.

Thus, the answer is:

$51.08