How to solve this word problem?

Question

Parents sometimes yell at their children for leaving the light on in their bedroom when they aren't in the room. If the child's room is lit with two 10 watt bulbs for one extra hour a day for everyday of the year (365), and the cost of energy is $0.068 per kilowatt*hour (kWh), how much money is wasted on lighting that isn't being used, to the nearest cent

Answer 1

The trick here is making all your units work out.  Remember that units cancel like fractions reduce.

 

Let's break it down.

 

In one day you have 2 10W bulbs lit for 1 hr.  That makes:

2 x 10W X 1 hr = 20 Watt-hours

 

Notice they give you a cost in kilowatt-hours, not watt-hours, so you have to convert.  Recall that 1000 of anything is 1 kilo of that thing.  So 1000 watts = 1 kilowatt.  Whenever you get an equality like that, you can make a fraction that will equal 1 out of it.  (1 kilowatt / 1000 watts) = 1.  And I can use that fraction to "cancel" and convert units - much the same way that you multiply 24 inches by (1 foot/12 inches) to get 2 feet.  During the multiplication, the unit of inches in the top and bottom cancel, and the units of the answer is in feet. 

 

So in our problem, 20 watt-hours x (1 kilowatt/1000 watts) = 0.02 kW-hr.  That is for one day.

 

Multiply by 365 days/year to get the kW-hrs in a year:

 

(0.02 kW-hr/day) x (365 days/year) = 7.3 kW-hr/year

 

Lastly, the cost is $0.063 per kW-hr, so again, multiply:

 

( 7.3 kW-hr/year ) x ( $0.063 / kW-hr ) = $0.46

 

Seems like a lot of yelling for nothing.  ... But don't tell the kids.  Once they are in college, they can figure it out!