# Question #24b8e

Jan 4, 2017

You should add 5000 kg of the 60 % manganese.

#### Explanation:

Let the mass of $\text{60 % Mn" = xcolor(white)(l) "kg}$

Look at the problem another way.

You are mixing 1000 kg of metal with $x \textcolor{w h i t e}{l} \text{kg of 60 % Mn}$ and getting $\text{(1000 +x) kg of 50 % Mn}$.

$\text{Mass of Mn in 60 % = mass of Mn in 50 %}$

$x \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{kg"))) × 60 color(red)(cancel(color(black)("% Mn"))) = (1000 +x) color(red)(cancel(color(black)("kg"))) × 50 color(red)(cancel(color(black)("% Mn}}}}$

$60 x = 50 \left(1000 + x\right) = \text{50 000} + 50 x$

$10 x = \text{50 000}$

$x = \frac{\text{50 000}}{10} = 5000$

Thus, you would add $\text{5000 kg of 60 % Mn}$ to 1000 kg of metal, and you would get $\text{6000 kg of 50 % Mn}$.

Check:

$\text{5000 kg of 60 % Mn}$ contains $\text{3000 kg of Mn}$, and $\text{6000 kg of 50 % Mn}$ also contains $\text{3000 kg of Mn}$.