Question #24b8e

1 Answer
Jan 4, 2017

Answer:

You should add 5000 kg of the 60 % manganese.

Explanation:

Let the mass of #"60 % Mn" = xcolor(white)(l) "kg"#

Look at the problem another way.

You are mixing 1000 kg of metal with #xcolor(white)(l) "kg of 60 % Mn"# and getting #"(1000 +x) kg of 50 % Mn"#.

#"Mass of Mn in 60 % = mass of Mn in 50 %"#

#x color(red)(cancel(color(black)("kg"))) × 60 color(red)(cancel(color(black)("% Mn"))) = (1000 +x) color(red)(cancel(color(black)("kg"))) × 50 color(red)(cancel(color(black)("% Mn")))#

#60x = 50(1000 + x) = "50 000" + 50x#

#10x = "50 000"#

#x = "50 000"/10 = 5000#

Thus, you would add #"5000 kg of 60 % Mn"# to 1000 kg of metal, and you would get #"6000 kg of 50 % Mn"#.

Check:

#"5000 kg of 60 % Mn"# contains #"3000 kg of Mn"#, and #"6000 kg of 50 % Mn"# also contains #"3000 kg of Mn"#.