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Aura currently pays $800 each month to rent her apartment.  Due to inflation, however, her rent is increasing by $50 each year.  Meanwhile, her monthly take-home pay is $1500 and she predicts that her monthly pay will only increase by $15 each year.  Assuming that her rent and take-home pay will continue to grow linearly, will her rent ever equal her take-home pay?  If so, when?  And how much will rent be that year?

Guest Jun 1, 2017
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Aura currently pays $800 each month to rent her apartment.  Due to inflation, however, her rent is increasing by $50 each year.  Meanwhile, her monthly take-home pay is $1500 and she predicts that her monthly pay will only increase by $15 each year.  Assuming that her rent and take-home pay will continue to grow linearly, will her rent ever equal her take-home pay?  If so, when?  And how much will rent be that year?

 

Let the number of years when her rent and her pay will equalize=N, so we have:

800 + 50N =1,500 + 15*12N

180N - 50N = 800 - 1,500

130N = -700 From this you can deduce that her rent will NEVER catch up with her pay.

Guest Jun 2, 2017
edited by Guest  Jun 2, 2017
edited by Guest  Jun 2, 2017

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