Question

A foundry has been commissioned to make souvenir coins. The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. How many kilograms of each alloy should be used to make 10 kilograms of the 40% silver alloy? 50% alloy = ? kg 25% alloy = ? kg

Answer 1

6 kilograms of 50% silver alloy and 4 kilograms of 25% silver alloy should be used.

Explanation

Suppose, the weight of the alloy with 50% silver content is $x$ kilograms.

As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be: $(10-x)$ kilograms

The percentage of silver content in the mixed alloy is 40%. So the equation will be .......

$0.50x+0.25(10-x)= 0.40(10)\\ \\ 0.50x+2.5-0.25x=4\\ \\ 0.25x= 4-2.5\\ \\ 0.25x=1.5\\ \\ x= \frac{1.5}{0.25}=6$

So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.