Question

160 kg of alloy of copper and aluminium contains 55% of aluminum. How much aluminum must be melted into it to make the alloy contain 75% of aluminum?

Answer 1

128 kg aluminum must be melted into it to make the alloy contain 75% of aluminum.

Explanation

160 kg of alloy of copper and aluminium contains 55% of aluminum.

So, the amount of aluminium in the alloy $=(160*0.55)kg= 88 kg$

Suppose,  $x$ kg aluminum must be melted into it to make a new alloy.

So, the amount of aluminium in the new alloy will be: $(88+x)kg$

and the total amount of the alloy will be: $(160+x)kg$

Given that, the new alloy contains 75% of aluminum. So, the equation will be....

$0.75(160+x)=88+x\\ \\ 120+0.75x=88+x\\ \\ 0.75x-x=88-120\\ \\ -0.25x=-32\\ \\ x=\frac{-32}{-0.25}=128$

So, 128 kg aluminum must be melted into it to make the alloy contain 75% of aluminum.