Mr. Vestas sells electricity from a wind turbine to his local utility. He receives 3¢ per kilowatt hour for the first 500 kilowatt hours, 2¢ per kilowatt hour for the next 1000 kilowatt hours, and 1¢ per kilowatt hour for each kilowatt hour thereafter. Mr. Vestas sold 1800 kilowatt hours last month. What was the average price per kilowatt hour the utility paid to Mr. Vestas last month, rounded to the nearest hundredth of a cent?

Step-by-step explanation:

We are expected to solve the weighted average price per kilowatt hour.

Step one:

The formula is  

W =∑wX/∑w

W=weighted average  

w=weights applied to x values

X=data values to be averaged

Step two:

given the total killowatt hour is 1800

the 1st = 500 at 3¢

2nd= 1000 at 2¢

3rd = (1800-1000+500) at 1¢ =(1800-1500) at 1¢ = (300) at 1¢

Step two:

Substituting into the expression we have

W =(500*3)+(1000*2)+(300*1)/500+1000+300

W=1500+2000+300/1800

W=3800/1800

W=2.11¢

The average price per kilowatt hour the utility paid to Mr. Vestas last month is 2.11¢

18/157

Step-by-step explanation

The key to solving this problem is to find the greatest common divisor of 72 and 628.

To find the greatest common divisor of 72 and 628, we list all of the factors of both numbers so we can compare the lists.

When we compared the factors of 72 (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and 628 (1, 2, 4, 157, 314, 628) we found that 4 is the largest factor that they have in common.

Since 4 is the largest common factor of 72 and 628, 4 is also the greatest common divisor of 72 and 628.

Now, we divide both the numerator and denominator in 72/628 by the greatest common divisor as follows:

Numerator: 72/4 = 18

Denominator: 628/4 = 157

Then, we put the numerator and denominator that we are left with back together to get our answer. 72/628 to the simplest form is: 18/157