What does culmination mean in this sentence
was the culmination of all his plans, all his yearning, all his work, all his waiting, for a long long year?

The answer is spray x: 10, spray y: 5, spray z: 12

a - number of gallons of chemical a
b - number of gallons of chemical b
c - number of gallons of chemical c

x - number of gallons of spray x
y -  number  of gallons of spray y
z -  number  of gallons of spray z

chemical         spray x           spray y           spray z
    a = 6           =         1/5x           +       0y           +           1/3z
    b = 8           =         2/5x         +       0y           +           1/3z
    c = 13         =         2/5x           +         y           +           1/3z

so:

1/5x + 1/3z = 6
2/5x + 1/3z = 8
2/5x + y + 1/3z = 13

multiply the first equation by (-1) and add it to the second equation: ž

- 1/5x - 1/3z = - 6
2/5x + 1/3z = 8

1/5x = 2
x = 2 * 5 = 10

from here:

1/5x + 1/3z = 6
x = 10

1/5 * 10 + 1/3z = 6
2 + 1/3z = 6
1/3z = 4
z = 4 * 3 = 12

1/5x + y + 1/3z = 13
x = 10
z = 12

2/5 * 10 + y + 1/3 * 12 = 13
4 + y + 4 = 13
8 + y = 13
y = 13 - 8 = 5