Question 39768: Hi, I will take my final exam for algebra this week and I came across this problem while studying. I would greatly appreciate it if you could answer my question.
Riding a bus to and from work costs you $5.50 round trip. You are thinking about buying a used car for $2500. Gas and maintenance will cost you about $.50 per trip. How many trips to work will it take to break even?
I set up the equations y= 11/2x and y= 2500 + 1/2x. Are these equations right? What do I do from here?
Found 2 solutions by checkley71, atif.muhammad:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! THE EQUATION SHOULD BE 5.50X=2500+.50X OR 5X=2500 OR X=2500/5 OR X=500 TRIPS
PROOF 5.50*500=2750 & 2500+.50*500=2500+250 OR 2500+250=2750
Answer by atif.muhammad(135) (Show Source):
You can put this solution on YOUR website!
Yes, I'd have thought they were right.
y= 11/2x and y= 2500 + 1/2x
We are trying to find out when we break even. Basically, we are trying to find out where the two lines intercept on the graph.
You could either plot and graph and find out from there, or take an algebraic approach!
Algebra:
When lines intercept on a graph, it means that they have common x and y co-ordinates.
Therefore, when the lines y= 11/2x and y= 2500 + 1/2x intercept, it must mean that:
y = y (We have to do it this way instead of x=x because we don't know x and that is what we're trying to find. If we do x=x, then we get rid of the x variable and there would be no point to our equation. Don't worry too much if you don't get this.)
5.5x = 2500 + 0.5x (I've used decimals instead of fractions, they're look better on the computer)
Let's solve this!
5x = 2500
x = 500
It will take 500 trips to work in order to break even!
Hope that helps!
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