<PRE><B>Question 999185</B>
let x be number of par3&#39;s, y be number of par4&#39;s, z = number of par5&#39;s, then
3x + 4y + 5z = 72
 x +  y +  z = 18
A) not enough info to answer question since we have two equations in three unknowns - we need three equations in three unknowns.
B) x + z = 8, now we have enough information
note that these are linear equations (exponents are 1)
C) augmented matrix is
3  4  5  72
1  1  1  18
1  0  1   8
Gaussian elimination method
subtract row 3 from row 2
3  4  5  72
0  1  0  10
1  0  1   8
multiply row 3 by 3 and subtract from row 1
0  4  2  48
0  1  0  10
1  0  1   8
multiply row 2 by 4 and subtract from row 1
0  0  2   8
0  1  0  10
1  0  1   8
divide row 1 by 2
0  0  1   4
0  1  0  10
1  0  1   8
subtract row 1 from row 3
0  0  1   4
0  1  0  10
1  0  0   4
***********************************************************
x = 4, y = 10, z = 4
***********************************************************
note that
x + z = 8
3*4 + 4*10 + 5*4 = 72
12 + 40 + 20 = 72
72 = 72
our answers check

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