need help to set up: How much of each is needed for mixture?

[phillipsjr9800]

A mixture of 12 gallons of chemical A, 16 gallons of chemical B, and 26 gallons of chemical C is required to kill a certain destructive crop insect. Commerical spray X contains 1, 2, and 2 parts of chemical A, B, and C respectively. Commercial spray Y contains onl chemical C. Commercial spray Z contains only chemical A and B in equal amounts. How much of each type of commerical spray is needed to obtain the desired mixture?

 

[stapel]

A mixture of 12 gallons of chemical A, 16 gallons of chemical B, and 26 gallons of chemical C is required to kill a certain destructive crop insect. Commerical spray X contains 1, 2, and 2 parts of chemical A, B, and C respectively. Commercial spray Y contains onl chemical C. Commercial spray Z contains only chemical A and B in equal amounts. How much of each type of commerical spray is needed to obtain the desired mixture?

You need to find the amounts of X, Y, and Z, so pick variables to represent what you need to find.

. . .gallons:
. . . . .Spray X: x
. . . . .Spray Y: y
. . . . .Spray Z: z

Then use the given relationships to create equations. You need twelve gallons of chemical A (or at least you need chemical A to be in the proper ratios with chemicals B and C). One gallon of Spray X is 1/5 chemical A (from the five parts, 1 + 2 + 2, listed in the mixture), one gallon of Spray Y contains none, and one gallon of Spray Z contains 1/2 gallon chemical A. Then:

. . . . .chemical A: (1/5)x + 0y + (1/2)z = 12

Follow the same reasoning in setting up equations for the other two chemicals. Then solve the system for the values of the variables, and thus the numbers of gallons required of each.

Eliz.