First student bought art, math and history books for $72. second student bought art, chemistry and history books for $80. third student bought chemistry, math and history books for $61. fourth student bought art, math and chemistry books for $57. how much does each book cost?

A + M + H = $72
A + C + H = $80
C + M + H = $61
A + M + C = $57

Difference between first student and second student = Math VS Chemistry
80 - 72 = 8
Therefore Chemistry = Math + $8
And Math = Chemistry - 8

Difference between second and third student = Art VS Math
80 - 61 = 19
Therefore Art = Math + 19
And Math = Art - 19

If C = M + 8 and A = M + 19
Then Art = Chemistry + 11
And Chemistry = Art - 11

Difference between third and fourth student = History VS Art
61 - 57 = 4
Therefore History = Art + 4
And Art = History - 4

Using trial and error, if A = 29
A + M + H = 72
29 + M + H = 72
29 + 10 + 33 = 71
Therefore,
Art = $29
Math = $10
History = $33

C = M + 8
C = 10 + 8
C = 19
So Chemistry = $19