Let the mass of "60 % Mn" = xcolor(white)(l) "kg"60 % Mn=xlkg
Look at the problem another way.
You are mixing 1000 kg of metal with xcolor(white)(l) "kg of 60 % Mn"xlkg of 60 % Mn and getting "(1000 +x) kg of 50 % Mn"(1000 +x) kg of 50 % Mn.
"Mass of Mn in 60 % = mass of Mn in 50 %"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".
