A dairy plant wants to prepare 60 litres of toned milk containing exactly 3\% fat by mixing three types of milk having 1\% fat, 3.5\% fat and 5\% fat respectively.
The quantity of 1\% fat milk used is twice the quantity of 5\% fat milk used.
(i) Frame three linear equations in the unknown quantities of the three types of milk.
(ii) Write the system obtained in part (i) in the symbolic form AX=B indicating the coefficient, variable and constant matrices.
(iii) Solve the system to determine the exact number of litres of each type of milk required.
(iv) Using your result from part (iii), verify that the final mixture indeed contains 60 litres and 3\% fat.