Question

A factory installs new machinery that will save 1250−38x dollars per year, where x is the number of years since installation. However, the cost of maintaining the new machinery is 81x dollars per year. Find the accumulated savings that will occur before the machinery should be replaced.

Answer 1

When should it be replaced?
when maintenace costs are >= savings

81x=1250-38x
119x=1250
or time=1250/119=10.5 years

Accumulated savings=sum(savings-cost) from n=1 to 10
= Sum1,10 (1250-38x-81x)
Add the series of answers up for all the years, and that is the total net savings over the course of purchasing the new machinery

check my work