50 kg of an alloy of lead and tin contains 60% of lead. How muh lead must be melted into it to make the alloy cantain 75% of lead?

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the amount of lead in the current alloy.
The alloy weighs 50 kg and contains 60% lead.

\[ \text{Amount of lead} = 60\% \text{ of } 50 \text{ kg} = \frac{60}{100} \times 50 = 30 \text{ kg} \]

### Step 2: Set up the equation for the new alloy.
Let \( x \) be the amount of lead that needs to be melted into the alloy. After adding \( x \) kg of lead, the total weight of the new alloy becomes:

\[ 50 \text{ kg} + x \text{ kg} \]

The total amount of lead in the new alloy will be:

\[ 30 \text{ kg} + x \text{ kg} \]

### Step 3: Set up the equation for the percentage of lead in the new alloy.
We want the new alloy to contain 75% lead. Therefore, we can set up the following equation:

\[ \frac{30 + x}{50 + x} = 0.75 \]

### Step 4: Solve the equation.
To eliminate the fraction, we can cross-multiply:

\[ 30 + x = 0.75(50 + x) \]

Expanding the right side:

\[ 30 + x = 37.5 + 0.75x \]

Now, isolate \( x \):

\[ 30 + x - 0.75x = 37.5 \]
\[ 30 + 0.25x = 37.5 \]
\[ 0.25x = 37.5 - 30 \]
\[ 0.25x = 7.5 \]
\[ x = \frac{7.5}{0.25} = 30 \]

### Step 5: Conclusion
Thus, the amount of lead that must be melted into the alloy to make it contain 75% lead is **30 kg**.

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