let

j = the number of juniors

s = the number of seniors

t = the number of freshman and sophomores

there are 60 players on a high school football team

j + s + t = 60

the ratio of juniors and seniors to freshmen and sophomores on the team is 2:3

(j + s) : t = 2 : 3

the ratio of juniors to seniors on the team is 1:2

j : s = 1 : 2

by solving the system of equations

j + s + t = 60

(j + s) : t = 2 : 3

j : s = 1 : 2

we find

j = 8

s = 16

there are 8 juniors and 16 seniors on the team.