50 kg of an alloy of lead and tin contains 60% of lead how much lead must be melted into it to make the alloy containing 75% of lead

1 answer

Let x be the amount of lead to be melted.

Initially, the alloy contains 0.6(50) = 30 kg of lead and 20 kg of tin.

After adding x kg of lead, the total amount of lead becomes 30 + x, and the total amount of alloy becomes 50 + x.

We want the resulting alloy to contain 75% lead, so:

(30 + x)/(50 + x) = 0.75

Solving for x:

30 + x = 0.75(50 + x)

30 + x = 37.5 + 0.75x

0.25x = 7.5

x = 30

Therefore, 30 kg of lead must be melted into the alloy to make it contain 75% lead.