Agroup of adults and students went on a class trip to washington, dc. the number of male students was 1 more than 7 times the number of adults. the number of female students was half the number of male students. if the total number of people who went on the trip is 82, find the numbers of male students and female students.

In equation, let x be the number of male students
a be the number of adults
y be the number of female students.
x= 7a+1
a= x/7 -1
y= x/2 or (7a + 1)/ 2

a + b = 82, let b be the number of students.
a + (x + y) = 82
a + [7a+1 + (7a+1)/2] = 82
a + [{2(7a+1) + 7a+1} / 2] = 82
a + [(14a +2 + 7a +1) / 2] = 82
a + [(21a + 3) / 2] = 82
(2a+ 21a + 3) / 2 = 82
(23a + 3) / 2 = 82
23a + 3 = 164
23a = 164 -3 
23a = 161
a = 7

x = 7(7) +1, 49+1 = 50 male students
y=x/2, 50/2, 25 female students

50(male students) + 25(female students)  + 7 (adults) = 82