# How much of a 75% copper alloy should be melted into 62 kg of a 35% copper alloy to produce an alloy which is 50% of copper?

Aug 6, 2015

$37.2$ kgm

#### Explanation:

Let the amount of 75% copper alloy be $x$ kgm.
then the total weight of the 50% alloy produced will be $x + 62$ kgm

The total copper in the combined alloy will be
$\textcolor{w h i t e}{\text{XXXX}}$$\left(0.75\right) x + \left(0.35\right) \left(62\right) = \left(0.50\right) \left(x + 62\right)$ kgm

$\textcolor{w h i t e}{\text{XXXX}}$$75 x + 2170 = 3100 + 50 x$

$\textcolor{w h i t e}{\text{XXXX}}$$25 x = 930$

$\textcolor{w h i t e}{\text{XXXX}}$$x = 37.2$