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