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?
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.