Marci Johnson uses gas to heat her home. She has accumulated the following infor
ID: 2586589 • Letter: M
Question
Marci Johnson uses gas to heat her home. She has accumulated the following information regarding her monthly gas bill and monthly heating degree-days. The heating degree-days value for a month is found by first subtracting the average temperature for each day from 65 degrees and then summing these daily amounts together for the month.
Month
Heating Degree-Days
Gas Bill
February
850
$129
April
300
$ 52
The equation representing the relationship between the gas bill (Y) and heating degree-days (X) is:
Select one:
A. Y = $60 + $0.14X
B. Y = $10 + $0.14X
C. Y = $10 + $0.14X
D. Y = $0.14
Month
Heating Degree-Days
Gas Bill
February
850
$129
April
300
$ 52
Explanation / Answer
Two types of cost are in it:
1. Variable cost per day
2. Fixed cost per day
Variable cost per day = (Gas bill for feb - gas bill for april) / (heating degree days for feb - april)
Variable cost = (129-52) / (850 - 300) = 77 / 550 = 0.14
Fixed Cost for feb = Gas bill - Heating degree days * variable cost
Fixed Cost for feb = 129 - 850*0.14 = 129 - 119 = $10
Similarly, for April
Fixed cost for april = 52 - 300*0.14 = 52 - 42 = $10
Hence our equation :
Y = $10 + 0.14X
So options B or C (as they both are same)