+22 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?
Use Desmos to graph it...
Rent will be equal 20 months in w/ $1800...
Equations are;
y=15x+1500
y=50x+800
Let the number of years when they will equalize =x
800+50x = 1500+15x
Solve for x:
50 x + 800 = 15 x + 1500
Subtract 15 x from both sides:
(50 x - 15 x) + 800 = (15 x - 15 x) + 1500
50 x - 15 x = 35 x:
35 x + 800 = (15 x - 15 x) + 1500
15 x - 15 x = 0:
35 x + 800 = 1500
Subtract 800 from both sides:
35 x + (800 - 800) = 1500 - 800
800 - 800 = 0:
35 x = 1500 - 800
1500 - 800 = 700:
35 x = 700
Divide both sides of 35 x = 700 by 35:
(35 x)/35 = 700/35
35/35 = 1:
x = 700/35
The gcd of 700 and 35 is 35, so 700/35 = (35×20)/(35×1) = 35/35×20 = 20:
Answer: |x = 20 Years.
Her rent will be: $800 + 20x50 =$800 + $1,000 =$1,800.
