Math

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?

asked by Jen
  1. 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+0-m = 8
    0+c+h+m = 61
    0+c-h+0 = -15

    subtract #2 from #3 and #4
    a+0+h+m = 72
    0+c+0-m = 8
    0+0+h+2m = 53
    0+0-h+m = -23

    add #3 to #4
    a+0+h+m = 72
    0+c+0-m = 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.

    posted by Steve
  2. 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

    posted by Scott

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