Mathematics, 18.09.2019 02:00 persis52

Amixture of 6 gallons of chemical a, 8 gallons of chemical b, and 13 gallons of chemical c is required to kill a destructive crop insect. commercial spray x contains 1, 2, and 2 parts respectively, of these chemicals. commercial spray y contains only chemical c. commercial spray z contains chemicals a, b, and c in equal amounts. how much of each type of commercial spray is needed to get the desired mixture?

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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

Answer from: Quest

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in conclusion, "ppl are so gay" due to their genetics.

Answer from: Quest

The solution to the system of equations (-2,2)

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Amixture of 6 gallons of chemical a, 8 gallons of chemical b, and 13 gallons of chemical c is requir...

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