SOLUTION: How many mg of a metal containing 45% nickel must be combined with 6 mg of pure nickel to form an alloy containing 78% nickel?

0.45x + 6 = 0.78*(x+6)


where x is the amount of metal under the question.


0.45x + 6 = 0.78x + 6*0.78


6 - 6*0.78 = 0.78x - 0.45 x

0.33x = 6 - 6*0.78 = 1.32  ====>  x =  = 4.


Answer.  4 mg of the 45% nickel.


Check.   0.45*4 + 6 = 7.8;   0.78*(4+6) = 7.8.    ! Correct !