Question 1196509
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I appreciate you showing your work and thought process, rather than just copy/pasting the problem only.


x = cost per day
y = cost per mile
Both costs are in dollars


Let's list the given facts
[1] Mateo was charged $111.00 for 3 days and 300 miles
[2] Dara was charged $207.00 for 5 days and 600 miles


Fact [1] gives us the equation
3x+300y = 111
since
3x = 3 times x = cost for the 3 days
300y = cost for the 300 miles
3x+300y = total cost


Fact [2] yields the equation 5x+600y = 207 through similar reasoning.


Here's our system of equations
3x+300y = 111
5x+600y = 207


Let's double the first equation to go from 3x+300y=111 to 6x+600y = 222


We arrive at this equivalent system of equations
6x+600y = 222
5x+600y = 207


Notice the 600y terms matching up. This allows us to cancel out the y terms if we subtract straight down
The x terms combine to 6x-5x = 1x = x
The right hand sides combine to 222-207 = 15


Therefore, x = 15


Then we can determine y
3x+300y = 111
3*15+300y = 111
45+300y = 111
300y = 111-45
300y = 66
y = 66/300
y = 0.22
You could use other equations previously mentioned involving x and y. 



We found that: x = 15 and y = 0.22
Therefore, it costs $15 per day and $0.22 per mile (aka 22 cents per mile).


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Check:


Mateo:
1 day = 15 dollars 
3 days = 15*3 = 45 dollars so far
1 mile = 0.22 dollars
300 miles = 300*0.22 = 66 dollars added on
45+66 = 111 dollars total for Mateo


Or we could say
3x+300y = 111
3*15+300*0.22 = 111
45+66 = 111
111 = 111
which confirms Mateo's equation


Let's follow a similar idea for Dara
5x+600y = 207
5*15+600*0.22 = 207
75+132 = 207
207 = 207
Her equation is confirmed as well.


Both equations are true for (x,y) = (15, 0.22)


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<font color=red>Answers:</font>
$15 per day
$0.22 per mile (aka 22 cents per mile)
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