word problem below

Question

Aurora 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 1,500 and she predicts that her monthly pay will only increase by $15 each year. Assuming that her rent and take home money 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 ? 

Answer 1

m represents the number of months

 

800 + 50m = 1500 + 15m        subtract 15m from both sides

800 + 35m = 1500                  subtract 800 from both sides

35m = 700                             divide both sides by 35

m = 20

 

Income and rent shall be equal after 20 months. At that time rent shall be $1800.