Quadratics

An apartment owner wants to increase the monthly rent from the 250 in x increases of10.

  1. What is the new price after the x increases of 10?</li> <li>If the number of apartments rented is 70 - 2x and the revenue is the number of apartments rented times the rent, what is the revenue?</li> <li>If the owner wants to receive17,980 per month, how many $10 increases can the owner make?

  2. 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 .
jim360
28 November 2012
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