his bill is $113. When he uses 1,500 kilowatt hours of electricity, his bill is $153. What is the monthly administration fee?

Question

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

Answer 1

Hello Ocean M., this math problem requires a multi-step solution. First, let's look at what information is given:

i. total is $113 for 1100 kwh plus an admin fee

ii. total is $153 for for 1500 kwh plus an admin fee

We are looking for the admin fee (not given)

Solution:

1. Set up a linear equation for both usages

General structure: monthly electric bill is determined by adding a flat administration fee ( I call it F) to the product of the number of kilowatt hours of electricity used and the cost per kilowatt hour (I call it c)

Monthly Bill total = F + kwh*c

Now we can set this up for the specific scenario given in the problem set:

i. Monthly bill total = $113, 1100kwh*c , F = unknown

113 = F+1100c

ii. Monthly bill total = $153, 1500kwh*c , F = unknown

$153 = F+1500c

Note: we have 2 unknown variables in each equation (F and c). However, the admin fee is constant for each bill and never changes. Hence, we assume that F in equation one and equation 2 are the same value. We can solve both equations for F, set the equations equal to one another and solve for c:

i. 113 = F+1100c ii. 153 = F+1500c

-1100c -1100c -1500c -1500c

113-1100c = F 153-1500c = F

F=F , therefore

113-1100c = 153-1500c

Now solve for c

113-1100c = 153-1500c

+1500c +1500c

113+400c = 153

-113 -113

400c = 40

400c/400 =40/400

c= 1/10 = 0.1

So now, the cost has been determined to be $0.10. We can use any of the first original equations, plug the value of c we just found and solve for F. The value must be the same in both equations. I will show the solution for both:

i. $113 = F+1100c ii. $153 = F + 1500c

$113 = F+ 1100 ($0.10) $153 = F + 1500 ($0.10)

$113 = F+$110 $153 = F + $150

-$110 -$110 -$150 -$150

$3 = F $3 = F

What is the monthly administration fee? Answer: the monthly administration fee is $3.

Hope this helps.

-Stephanie G.