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average problem

by rupsk » Fri Jul 22, 2011 3:42 pm
The cost of 1 unit of electricity during a 4 year period is given below. Year 1, $1 per unit. Year 2, $1.5 per unit. Year 3, $1.2 per unit. Year 4, $2 per unit. If a factory spent equal dollars each year for electricity what was the average cost of a unit of electricity during the 4 year period?

A. $ 1.333

B. $1.250

C. $1.425

D. $1.175

e. $1.500

my answer was c but correct ans is a. please help to understand my mistake.
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by goalevan » Fri Jul 22, 2011 4:05 pm
Year 1: $1/unit
Year 2: $1.5/unit
Year 3: $1.2/unit
Year 4: $2/unit

The LCM of 10 (2*5), 15 (3*5), 12 (2*2*3), and 20 (2*2*5) is 2*2*3*5 = 60, so $60/10 = $6 could have been the spending for each year.

$1/unit * 6 units = $6
$1.5/unit * 4 units = $6
$1.2/unit * 5 units = $6
$2/unit * 3 units = $6

The weighted average will be the sum of the electricity spending for each year divided by the number of units:
(6 + 6 + 6 + 6) / (6 + 4 + 5 + 3) = 24 / 18 = 4/3 = $1.333/unit

A
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by rupsk » Fri Jul 22, 2011 8:12 pm
Why you have taken LCM? I just did normal average of 4 numbers. Please explain me the logic behind it.
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by top_business_2011 » Sat Jul 23, 2011 12:17 am
rupsk wrote:The cost of 1 unit of electricity during a 4 year period is given below. Year 1, $1 per unit. Year 2, $1.5 per unit. Year 3, $1.2 per unit. Year 4, $2 per unit. If a factory spent equal dollars each year for electricity what was the average cost of a unit of electricity during the 4 year period?

A. $ 1.333

B. $1.250

C. $1.425

D. $1.175

e. $1.500

my answer was c but correct ans is a. please help to understand my mistake.
Here is my take:

Total cost year 1 = 1X
Total cost year 2 = 1.5Y
Total cost year 3 = 1.2Z
Total cost year 4 = 2M, Where, X, Y, Z, and M represent the units of electricity purchased in year 1, year 2,year 3, and year 4 respectively.

As stated in the question, 1X = 1.5Y = 1.2Z =2M
And let's represent them all by another variable 'a'
Hence, to get the weighted average, add all the cost and divide that by the sum of X, Y, Z, and M.

1X + 1.5Y + 1.2Z + 2M = a + a + a + a = 4a so this is our numerator.
Now let's find X,Y,Z, and M.
1X=a
X=a
1.5Y= a
Y=2a/3
1.2z = a
z= 5a/6
2m = a
m= a/2
Therefore, the weighted average is equal to: (4a)/[a +(2a/3)+ (5a/6) + (a/2)]
= 4a/3a = 1.333..
But, I feel that the question should have asked for the approximate value as there is no value from the choices that's equal to our answer. Or is the measurement of the dollar a discrete variable? If that is so, then Ok. Hahaha....
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by goalevan » Sat Jul 23, 2011 9:41 am
Hello rupsk,

The question is asking for a weighted average cost per unit of electricity for the 4-year period.

The average, weighted on the number of units, will be in the form:

Total cost / total number of units

Total cost =
1stYr cost/unit * 1stYr units = 1stYr cost
+ 2ndYr cost/unit * 2ndYr units = 2ndYr cost
+ 3rdYr cost/unit * 3rdYr units = 3rdYr cost
+ 4thYr cost/unit * 4thYr units = 4thYr cost

Number of units =
1stYr units
+ 2ndYr units
+ 3rdYr units
+ 4thYr units

I took the LCM of 10, 12, 15, and 20 because it allowed me to quickly find a common total cost for each year (this turned out to be $6), from which I calculated the units used in each year to bring the total cost to that amount (6 units, 4 units, 5 units, 3 units per year, respectively). These yearly units I then used to weight the average.

(6 + 6 + 6 + 6) / (6 + 4 + 5 + 3) = $1.333
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by rupsk » Sat Jul 23, 2011 9:44 am
thanks got it.
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