The local florist made three sets of fertiliser mix (A, B and C) which she sold in 1 litre bags. To make mix A, she used 100 g of potash, 600 g of nitrogen and 600 g of blood and bone. At the end of the week she had sold 345 bags of mix A. For mix B, she used 300 g of potash, 200 g of nitrogen and 600 g of blood and bone; she sold 295 bags of mix B. Mix C, consisted of 400 g of potash, 100 g of nitrogen and 600 g of blood and bone, and 290 bags of mix C were sold. In fact every bag made up was sold. How many kilograms of potash, nitrogen and blood and bone, respectively, did she use?
I got the equations below:
$$0.1p+0.6n+0.6b= 1.3 kg\cdot 345\ bags$$
$$0.3p+0.2n+0.6b=1.1kg\cdot 295\ bags$$
$$0.4p+0.1n+0.6b=1.1kg\cdot 290\ bags$$
Using matrix (reduced row echelon form) or simply 3 variable equations.
I got the following answer: $p=510 ,n=565, b=97.5$ but the answer is incorrect. Can someone guide me on where did i go wrong? Thanks a lot.
Your three equations are not correct. They should be instead:
$$0.1p+0.6n+0.6b= 345$$
$$0.3p+0.2n+0.6b=295$$
$$0.4p+0.1n+0.6b=290$$
because each bag is $1$ litre.
I get that $p=150, n=200$ and $b=350$.