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.