Question 1198749
rent = 600 per month plus 60 for each day it is used.
buy = 4,000 per year plus 80 for each day it is used.


the yearly cost for renting is equal to 600 * 12 = 7200 plus 60 for each day it is used.


the yearly cost for buying is 4,000 plus 80 for each day it is ued.


your inequality is 7200 + 60x < 4000 + 80x
x is the  number of days.
subtract 4000 from both sides of the equation and subtract 60x from both sides of the equation to get:
3200 < 20x
divide both sides of the equation by 20 to get:
160 < x


the machine would have to be used more than 160 days for the rental option to be cheaper than the buy option.


at 160 days, the rental option is 7200 + 60 * 160 = 16800
at 160 days, the buy option is 4000 _+ 80 * 160 = 16800


that'a the break even point.


at 161 days, the rental option is 7200 + 60 * 161 = 16860
at 161 days, the buy option is 4000 + 80 * 161 = 16880
the rental option is cheaper than the buy option by 20.


at 300 days, the rental option is 7200 + 60 * 300 = 25200
at 300 days, the buy option is 4000 + 80 * 300 = 28000.
the rental option is cheaper than the buy option by 2800.


2800 / (300 - 160) = 2800 / 140 = 20.
the rental option is cheaper than the buy option by 20 dollars for each day over 160.


the equations can be graphed as shown below:


<img src = "http://theo.x10hosting.com/2022/113004.jpg">