A service company recently revised its call-routing procedures in an attempt to increase
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The solution depends on the value of 
. To make things simple, assume 
. The homogeneous part of the equation is
and has characteristic equation
which admits the characteristic solution
.
For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be
. Then
So you have
This means
and so the general solution would be
and has characteristic equation
which admits the characteristic solution
For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be
So you have
This means
and so the general solution would be
So since you gave all of the equations of everyone's amount that they put in, it saves some work.
Let's add up everyone's contribution and then solve for x:
Then since we know the television costs $2,000, we can set this expression equal to that and simplify terms. Then we can solve for x:
So since Ronnie put in 'x', we can say that Ronnie paid $70.
Since Mark put in '2x + 500', we can plug in 70 for x to find that Mark paid $640.
And since Lisa put in '650 + 2x + 500', we can plug in 70 for x again to find that Lisa paid $1,290.