Question

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?​

Answer 1

By equations, we can put this.

Rent: 50x + 800

Take-home Pay: 15x + 1500

So we need them to be together, which means we combine the two equations.

50x + 800 = 15x + 1500

minus 800 by both sides

50x = 15x + 700

minus 15x by both sides

35x = 700

divide 35 by both sides

x = 20

Double check:

50(20) + 800 = 15(20) + 1500

1000+800 = 300 + 1500

1800 = 1800 √