Question

determining unknowns in a contextual system of equations
bryans 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? $

Explanation:

Step1: Set up equations

Let $x$ be the cost per kilowatt - hour and $y$ be the flat administration fee.
We get the system of equations:

$$\begin{cases}1100x + y=113\\1500x + y = 153\end{cases}$$

Step2: Subtract the first equation from the second

$(1500x + y)-(1100x + y)=153 - 113$
$1500x + y-1100x - y=40$
$400x=40$, so $x = 0.1$

Step3: Substitute $x$ into the first equation

Substitute $x = 0.1$ into $1100x + y=113$
$1100\times0.1+y=113$
$110 + y=113$
$y=113 - 110=3$

Answer:

$3$