Mixture Calculation to Kill Destructive Crop Insect

To solve the problem of creating the ideal mixture to kill the destructive crop insect, we need to first analyze the chemical composition of each commercial spray. Commercial spray X contains 1 part of chemical A, 2 parts of chemical B, and 2 parts of chemical C. Spray Y consists of chemical C only, while spray Z contains equal amounts of chemicals A and B.

From the given requirements of 14 liters of chemical A, 19 liters of chemical B, and 29 liters of chemical C, we can set up a system of equations to represent the relationships between the spray amounts:

Equations for Spray Amounts:

X + Z = 14 (for chemical A)

2X + Z = 19 (for chemical B)

2X + Y = 29 (for chemical C)

By solving these equations simultaneously, we can find the values for X, Y, and Z, which represent the amounts of commercial sprays X, Y, and Z required to create the desired mixture. If the system is dependent, we can introduce a variable, such as 'a' for Z, and express sprays X and Y in terms of 'a' to maintain the relationships between the chemicals.

Ultimately, the key to successfully achieving the optimal combination lies in accurately calculating the amounts of each commercial spray based on their chemical compositions and the desired mixture requirements. By following the systematic approach of solving a system of linear equations, we can determine the precise quantities of sprays X, Y, and Z needed to effectively eliminate the destructive crop insect.