SOLUTION: I have been trying to turn this word problem into a linear equation for a while and have had no luck. Can someone please help? A downtown employee is looking for the best opti

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Question 773335: I have been trying to turn this word problem into a linear equation for a while and have had no luck. Can someone please help?

A downtown employee is looking for the best option for parking a car during a 5 day work week. Garage A offers unlimited parking at a flat rate $150.00 per month. Garage B offers an hourly rate of $2.00 for parking. Which option is best for the employee on a monthly basis?
The employee plans on parking in the garage 5 days a week for 8 hours a day. He will be parking 160 hours per month. This is a word problem that I had to come up with on my own make 2 linear equations out of it and then graph it and show where they intercept.
Any help would be appreciated. Thank you!

Answer by ramkikk66(644)   (Show Source): You can put this solution on YOUR website!
Let the parking hours be x per month, and the fee be y.
In the first case, fee is fixed and not dependent on number of hours.
i.e. y is independent of x. The equation in this case is y = 150.
In the second case, the fee is $2 per hour. Or the equation is y = 2*x.
Taking the two equations
 ----> (1)
 ----> (2)
They intersect at a point where 2*x = 150 or x = 75.
Obviously, if the parking hours > 75, he has to pay a fee of more than the flat
fee of 150. Since he needs 160 hours of parking per month, the first option of
$150 is clearly better. Option 2 is better only if he is parking for < 75 hours
per month.
Hope you got it :) See the graph below.



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