Math
posted by Jen
First student bought art, math and history books for $72. a+m+h=72
Second student bought art, chemistry and history books for $80. a+c+h=80
Third student bought chemistry, math and history books for $61. c+m+h=61
Fourth student bought art, math and chemistry books for $57. a+m+c=57
How much does each book cost?
How would you do this without guess and check?

Steve
You have 4 equations in 4 unknowns, so use elimination or substitution. For example,
a+0+h+m = 72
a+c+h+0 = 80
0+c+h+m = 61
a+c+0+m = 57
subtract #1 from #2 and #4
a+0+h+m = 72
0+c+0m = 8
0+c+h+m = 61
0+ch+0 = 15
subtract #2 from #3 and #4
a+0+h+m = 72
0+c+0m = 8
0+0+h+2m = 53
0+0h+m = 23
add #3 to #4
a+0+h+m = 72
0+c+0m = 8
0+0+h+2m = 53
0+0+0+3m = 30
so, m=10
use that to fill in the other values, working your way up the rows. 
Scott
subtracting 1st from 2nd ... c  m = 8
... c = m + 8
substitute into 3rd ... 2m + h = 53 (A)
substitute into 4th ... 2m + a = 49 (B)
subtracting ... h  a = 4
adding to 1st ... 2h + m = 76
... multiply by 2 ... 4h + 2m = 152
... subtract A ... 3h = 99 ... h = 33
substitute to find m , c , and a
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