SOLUTION: A car rental company has two rental rates. Rate 1 is $63 per day plus $0.18 per mile. Rate 2 is $126 per day plus $0.09 per mile. If you plan to rent for one week, how many miles w

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Question 277289: A car rental company has two rental rates. Rate 1 is $63 per day plus $0.18 per mile. Rate 2 is $126 per day plus $0.09 per mile. If you plan to rent for one week, how many miles would you need to drive to pay less by taking Rate 2?
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
y = mx + b is the standard slope-intercept formula for a line
we can put the information given into two equations in slope-intercept format
R1 = .18x + 63, where x= miles driven
R2 = .09x + 126
.
we can graph the two lines to see where they cross
R1 = red line, which has a steeper slope
R2 = green line, which has a lower slope
.

.
it appears the lines cross at about x=700 (or 700 miles driven)
.
of course, we know R1 and R2 really are just other names for 'y'
.
y = .18x + 63
y = .09x + 126
.
multiplying both equations by 100 to remove decimals
100y = 18x + 6300
100y = 9x + 12600
.
rearranging to put into simultaneous equation format
.
-18x + 100y = 6300
-9x + 100y = 12600
,
subtracting the second equation from the first
-9x = -6300
.
dividing both sides by -9
x = 700
.
so we confirm that the two lines cross at x=700.
.
that means that at a distance driven 'x' of 700, the cost of the two rental plans is the same.
.
but after that point, the line with lower slope rises more slowly, which means the other plan (the one with the steeper slope) is more expensive and getting more expensive for every mile driven > 700.
.
Answer:
You need to drive more than 700 miles for Rate 2 to be less expensive than Rate 1.
.

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