Question

In two alloys, the ratios of copper to zinc are $5:2$ and $3:4$ (by weight). How many kg of the first alloy and of the second alloy should be alloyed together to obtain $28$ kg of a new alloy with equal contents of copper and zinc?

Answer 1

Let $x$ be the amount of first alloy mixed

let $y$ be the amount of second alloy mixed

Copper in $1^{st}$ alloy $=\frac{5}{7}x$

Copper in $2^{nd}$ alloy $=\frac{3}{7}x$

Total copper $=\frac{5x+3y}{7}$

Zinc in $1^{st}$ alloy $=\frac{2}{7}x$

Zinc in $2^{nd}$ alloy $=\frac{4}{7}x$

Total Zinc $=\frac{2x+4y}{7}$

Both copper & zinc should be in $|:|$ ratio $\frac{\frac{5x+3y}{7}}{\frac{2x+4y}{7}}=1$

$5x+3y=2x+4y$

$3x=y$ $⟶\left(I\right)$

we know both alloy should make $28kg$

$x+y=28$ $⟶\left(II\right)$

where $y=3x$

$x+3x=28$

$x=7kg$ $⟶1^{st}$ alloy

$y=21kg$ $⟶2^{nd}$ alloy