For Christmas, a family decorated their home with Christmas lights.

Question

For Christmas, a family decorated their home with Christmas lights. They installed two types of lights: string lights and icicle lights. During Christmas Day: • Each string light has a power of 0.6 watts and runs for 10 hours.

• Each icicle light has a power of 2 watts and runs for 12 hours.

• The family uses 250 string lights and 20 icicle lights.

• The total electricity rate is $0.18 per kilowatt-hour (1 kilowatt = 1000 watts).

Based on the information provided, select for  Energy  the total energy consumption (in kilowatt-hours) of all icicle lights over their full 12-hour runtime on Christmas Day and select for  Cost  the total electricity cost (in dollars) of running all string lights for their full 10-hour runtime on Christmas Day.

Bunuel · Accepted Answer

Official Solution:

Energy (icicle lights):

Each icicle light: 2 * 12 = 24 watt-hours = 0.024 kWh

20 icicle lights: 20 * 0.024 = 0.48 kWh
 
 Cost (string lights):

Each string light: 0.6 * 10 = 6 watt-hours = 0.006 kWh

250 string lights: 250 * 0.006 = 1.5 kWh

Cost: 1.5 * 0.18 = 0.27 dollars

Correct answer:

Energy  "0.48"

Cost  "0.27"

Bismuth83 · Answer

1. Each icicle light uses  2 \ watts * 12 \ hours = 24 Wh = 0.024 kWh . Since there are 20 of them, then together they use up  0.024 kWh * 20 = 0.48 kWh .

2. Let’s first find the total amount of energy consumed by the string lights and then we can determine how much that energy would cost. Each string light uses  0.6 \ watts * 10 \ hours = 6 Wh = 0.006 kWh . Since there are 250 of them, then together they use up  0.006 kWh * 250 = 1.5 kWh . The cost per kWh is $0.18, so the total cost will be  \$0.18 * 1.5 = \$0.27 .

3. Our answer will be:   Energy - 0.48 and Cost - 0.27  .

Edoua · Answer

Bismuth83

It’s mentioned 
1) the total cost per KWh is $0.18 
2)the use both type of light (no where it’s mentioned separately or not)

Let’s assume they both type at the same time 
This mean $0.18 per KWh is constituted by both types of light 
(Per hour , icicle can contribute $x and string lights (0.18-x)

So to find the total amount by string lights on that day, we can’t simply multiply $0.18*1.5 (because this will means each type individually contributed the same amount. Only possible if both type didn’t work together) —> that is not mentioned in the statement.

Is there something I’m missing?

Bismuth83 · Answer

I think you might be confused with the terms for power and energy. Let me try to explain it better without units.

Over the day, string lights consume in total  E_1 , which is an amount of energy. Similarly, icicle lights consume in total  E_2 .

We're given that the cost for energy consumption is $0.18 per unit (or 1). So, the total cost for string lights would be the cost rate multiplied by how much is being consumed in total. This is: $0.18   *    E_1 .

I hope that helped! Feel free to ask more questions.

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For Christmas, a family decorated their home with Christmas lights.

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Energy	Cost
		0.24
		0.27
		0.36
		0.48
		0.50
		0.65

Energy	Cost
		0.24
		0.27
		0.36
		0.48
		0.50
		0.65

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