Let

x = score of Anita

y = score of Miguel

z = score of Cheri

t = score of Jake

x = y - 18 (Anita scored 18 less than Miguel)

z = 2*x - 16 (Cheri's score was 16 less than twice Anita's)

z = t + 21 (Cheri outscored Jake by 21)

x + y + x + t = 529 (The total scored by all four kids is 529)

If we solve this system of equations we find the results

x = 548/5 = 109.6 is the score of Anita

y = 638/5 = 127.6 is the score of Miguel

z = 1016/5 = 203.2 is the score of Cheri

t = 911/5 = 182.2 is the score of Jake