Question 899897
3b+0*h+5p=226
7b+2h+0*p=227
0*b+8h+5p=322
3,0,5,226
7,2,0,227
0,8,5,322

divide row 1 by 3
1,0,5/3,226/3
7,2,0,227
0,8,5,322

add  down (-7) *row 1 to row 2
1,0,5/3,226/3
0,2,-35/3,-901/3
0,8,5,322

add  down (0) *row 1 to row 3
1,0,5/3,226/3
0,2,-35/3,-901/3
0,8,5,322

divide row 2 by 2
1,0,5/3,226/3
0,1,-35/6,-901/6
0,8,5,322

add  down (-8) *row 2 to row 3
1,0,5/3,226/3
0,1,-35/6,-901/6
0,0,310/6,9140/6

divide row 3 by 155/3
1,0,5/3,226/3
0,1,-35/6,-901/6
0,0,1,13710/465

We now have the value for the last variable.
We will work our way up and get the other solutions.

add up  (35/6) *row 3 to row 2
1,0,5/3,226/3
0,1,0,24354/1116
0,0,1,914/31

add up  (-5/3) *row 3 to row 1
1,0,0,7308/279
0,1,0,1353/62
0,0,1,914/31

add up  (0) *row 2 to row 1
1,0,0,50344/1922
0,1,0,1353/62
0,0,1,914/31

final
1,0,0,812/31
0,1,0,1353/62
0,0,1,914/31

1,0,0,812/31 = 26.1935484
0,1,0,1353/62 = 21.8225806
0,0,1,914/31 = 29.483871
"812/31","1353/62","914/31"
(812/31,1353/62,914/31)

26.1935484+21.8225806+29.483871=77.5
add all three to get 77.5 for one of each