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Question 252232: Suppose that the electricity bill is determined only by multiplying the number of kilowatt hours used by the cost per kilowatt hour. Last February Ben’s electric bill was $50. This February the number of kilowatt hours used was 20% higher and the rate per kilowatt hour was 8% lower. To the nearest percent, select the percentage by which his electric bill has changed.
A. 12% increase B. 10% increase C. 0% D. 10% decrease E. 12% decrease
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! c = cost per kilowatt hour
k = number of kilowatt hours.
you get:
c*k = 50
that was last february.
this february the bill is:
.92*c*1.2*k = ?????
this is the same as:
.92*1.2*c*k = ?????
we know that c*k is equal to $50.00, so the equation becomes:
.92*1.2*50 = ?????
this becomes:
.92*1.2*50 = 55.2
this years bill should be $55.20
55.2/50 = 1.104 - 1 = .104 * 100% = 10.4%.
rounded to the nearest integer, this because a 10% increase which would be selection B.
example:
assume the cost per kilowatt hour was 20 cents / 100 = $.20
if the bill was 50, then the kilowatt hours were 250.
drop the cost by 8% to get c = .2 * (1-.08) = .2 * .92 = .184 per kilowatt hour.
raise the number of kilowatt hours by 20% to get 250 * (1 + .2) = 250 * 1.2 = 300 kilowatt hours.
figures for last february were:
c = .2
k = 250
figures for this february are:
c = .184
k = 300
.184 * 300 = 55.2
cost for last february was $50.00
cost for this february is $55.20
55.2 / 50 = 1.104 - 1 = .104 * 100% = 10.4% rounded to the nearest integer = 10%.
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