let

x = the score from the first exam

y = the score from the second exam

z = the score from the third exam

Aura took three biology exams and has an average score of 86

(1/3)(x + y + z) = 86

her second exam score was 6 points better than her first,

y = 6 + x

and her third exam score was 3 points better than her second exam

z = 3 + y

by solving the system of equations

(1/3)(x + y + z) = 86

y = 6 + x

z = 3 + y

we find

x = 81 points

y = 87 points

z = 90 points

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Aura scored 81 points on her first exam, 87 points on her second exam and 90 points on her third exam.