Question 1171112
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x = number of miles driven
y = total cost


First Plan:
If you drive 1 mile, then you are charged $0.70
If you drive x miles, then you are charged 0.70x dollars. This is on top of the $45 initial fee. In total, you pay y = 0.70x+45 for the first plan.



Second Plan: 
There are no initial costs, but the cost per mile is higher. The equation here is y = 0.90x


We have this system of equations
y = 0.70x+45
y = 0.90x


Since y is equal to both 0.70x+45 and 0.90x, this means we can equate the right hand sides and solve for x


0.90x = 0.70x+45
0.90x-0.70x = 45
0.20x = 45
x = 45/0.20
x = 225


The two plans cost the same when you drive exactly 225 miles.


Plug this x value into either equation to find y
y = 0.70x+45 = 0.70*225+45 = 202.50
or
y = 0.90x = 0.90*225 = 202.50


You only need to pick on one equation, but doing both helps show that x = 225 leads to the same y value. This confirms our answers.


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Answers:
The plans cost the same when you drive 225 miles.
The cost is $202.50 when the plans cost the same.
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