A farmer is offered three types of lawn fertiliser, each containing nitrogen, phosphate, and potassium Type A is labeled 24-12-0. type B is 4-4-18. and type C is 18-10-9 These labels means, for example, that type C contains l8% nitrogen 10% phosphate, and 9% potassium by weight. The fanner wants to know how many kilograms of each of the three types of fertiliser are needed in order to fertilise a field with exactly 54kg of nitrogen 34kg of phosphate, and 63kg of potassium Express the fanner's problem using a system of linear equations, and find all solutions to the system Each of the three types of fertiliser costs $2.40 per kilogram What is the cheapest way for the fanner to fertilise the field, and what combination of fertiliser types does it involve?
Show transcribed image textA farmer is offered three types of lawn fertiliser, each containing nitrogen, phosphate, and potassium Type A is labeled 24-12-0. type B is 4-4-18. and type C is 18-10-9 These labels means, for example, that type C contains l8% nitrogen 10% phosphate, and 9% potassium by weight. The fanner wants to know how many kilograms of each of the three types of fertiliser are needed in order to fertilise a field with exactly 54kg of nitrogen 34kg of phosphate, and 63kg of potassium Express the fanner's problem using a system of linear equations, and find all solutions to the system Each of the three types of fertiliser costs $2.40 per kilogram What is the cheapest way for the fanner to fertilise the field, and what combination of fertiliser types does it involve?