Forest Middle School had 760 middle school students. They are hoping to increase their enrollment by 15% next year. How many total middle school students should they have enrolled next year

To find the increase in enrollment, multiply the current enrollment by 15/100: 760 students * 15/100 = <<760*15/100=114>>114 students

Then add the increase to the current enrollment to find the total enrollment: 760 students + 114 students = <<760+114=874>>874 students. Answer: \boxed{874}.