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katen-ka-za
12 days ago
9

Bryan’s monthly electric bill is determined by adding a flat administration fee to the product of the number of kilowatt hours o

f electricity used and the cost per kilowatt hour. When he uses 1,100 kilowatt hours of electricity, his bill is $113. When he uses 1,500 kilowatt hours of electricity, his bill is $153. What is the monthly administration fee?
Mathematics
2 answers:
Inessa [12.5K]12 days ago
6 0
We will create the equations for this scenario:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
Find z: Monthly administration fee is represented by z, which is the question of this problem.
The amounts of kilowatt hours consumed are 1100 and 1500 respectively.
The cost for each kilowatt hour is denoted by y, although its value is not required for this math problem, we can compute it regardless.
This results in a system of two equations with two unknowns, which can be solved using the substitution method:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
----------------------------
(1) z = 113 - 1100*y [substituting z (right side) into equation (2) instead of z]:
(2) 1500*y + (113 - 1100*y) = 153
-------------------------------------------------
(1) z = 113 - 1100*y
(2) 1500*y + 113 - 1100*y = 153
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y + 113 = 153
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y = 153 - 113
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y = 40
------------------------------------------------
(1) z = 113 - 1100*y
(2) y = 40/400
------------------------------------------------
(1) z = 113 - 1100*y
(2) y = 1/10
------------------------------------------------
by placing the calculated value of y back into equation (1), we can find z:
(1) z = 113 - 1100*(1/10)
(1) z = 113 - 110
(1) z = 3 dollars serves as the monthly fee.
Zina [12.3K]12 days ago
5 0

Solution:

3

Detailed explanation:

correct on ed (:

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