Question 1161268
{{{d}}}= daily fee in $ per day
{{{m}}}=mileage fee in $ per mile
 
For Barney, the equation is
{{{3d+300m=120}}}.
Multiplying both sides of that equation times {{{2}}} we get
{{{6d+600m=240}}} .
 
For Mary, the equation is
{{{5d+600m=210}}} .
Subtracting from the previous equation
(or multiplying times {{{-1}}} and combining equations we get
{{{6d+600m-5d-600m=240-210}}} ,
which simplifies to
{{{highlight(d=30)}}} .
We have "eliminated" variable {{{m}}} to find the value for {{{d}}} .
That was quite easy.
It would have been a lot more cumbersome to try the other way around.
 
Hopefully the elimination requirement is considered satisfied,
and we would be allowed to substitute into {{{3d+300m=120}}}.
the value found for {{{d}}} to get
{{{3*30+300m=120}}} ,
which simplifies to
{{{90+300m=120}}}
and solve going through
{{{300m=120-90}}} and {{{300m=30}}}
to get to
{{{m=30/300}}} and {{{highlight(m=0.1)}}} .
So, the daily charge is {{{highlight("$30")}}} per day, and 
the mileage charge is {{{highlight("$0.10")}}} per mile.