solve for x

45% x + 6 = 78% (x+6)

--Let x represent pure nickel, then 78%(x + 6mg) = 45%x + 6mg

Multiplying both sides by 100 to remove percentages, 78(x + 6mg) = 45x + 600mg

Simplifying left hand side, 78x + 468 = 45x + 600mg

Transposing like terms, 78x - 45x = 600mg - 468mg

Subtracting like terms, 33x = 132

Dividing both sides by 33, x = 4mg

Answer: 4mg 45% nickel must be combined with 6mg pure nickel to form a 78% nickel alloy.