Quadratics
An apartment owner wants to increase the monthly rent from the 10.
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What is the new price after the x increases of
17,980 per month, how many $10 increases can the owner make?
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What will be the monthly rent?
Answers
A: (250+10x) dollars. Hopefully this is self-evident, once it's clear what the question is trying to say.
B: Revenue = (rent per apartment) * (number of apartments rented) = (250+10x)*(70-2x). Again this just comes from taking the question literally and replacing revenue and rent by their algebraic expressions, given to us.
C: Now we want to make a revenue of 17,980 per month, and we now how much revenue is made per month from Part B. So we set the two equal to each over and get that:
Now we have to expand out the brackets:
And this is still equal to 17,980. We now subtract 17,980 from both sides to give:
Now we divide everything by 20 and also multiply by -1, just to simplify things a little:
We've reduced the problem to a relatively simple quadratic equation. You should be able to check that this factorises nicely:
So that x = 6 or x = 4 solves the problem. Hence Our apartment owner can make 4 or 6 increases of $10.
D: In turn, the total rent per apartment is either 290 dollars if , or 310 dollars if .
28 November 2012
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