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
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.
To determine how much lead must be melted into the alloy to achieve a lead concentration of 75%, we need to follow these steps:
Step 1: Calculate the current amount of lead in the alloy.
Given that the original alloy weighs 50 kg and contains 60% of lead, we can calculate the amount of lead in the alloy as:
Lead in alloy = 50 kg * (60/100) = 30 kg
Step 2: Determine the desired amount of lead in the final alloy.
Since we want the alloy to contain 75% of lead, we can calculate the desired amount of lead in the final alloy as a percentage of the total weight.
Desired lead in alloy = 50 kg * (75/100) = 37.5 kg
Step 3: Calculate the additional lead required.
The additional lead required is the difference between the desired amount of lead in the final alloy and the current amount of lead in the original alloy.
Additional lead required = Desired lead in alloy - Lead in alloy
Additional lead required = 37.5 kg - 30 kg = 7.5 kg
Therefore, you need to melt an additional 7.5 kg of lead into the alloy to achieve a lead concentration of 75%.