To make a benzene soluble cement, `60 g` rosion is melted in an ion pot and `68 g` beeswax and `12 g` shellac are added. How much of shellac should be taken to makes `35 g` cement?

Explanation

To solve the problem, we need to determine how much shellac is required to make 35 grams of benzene soluble cement based on the original mixture. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the total mass of the original cement mixture.
The original mixture consists of:
- Rosin: 60 g
- Beeswax: 68 g
- Shellac: 12 g

Total mass of the original cement mixture:
\[ \text{Total mass} = \text{mass of rosin} + \text{mass of beeswax} + \text{mass of shellac} \]
\[ \text{Total mass} = 60 \, \text{g} + 68 \, \text{g} + 12 \, \text{g} = 140 \, \text{g} \]

### Step 2: Determine the proportion of shellac in the original mixture.
The mass of shellac in the original mixture is 12 g. To find out how much shellac is needed for 35 g of the cement, we can set up a proportion.

### Step 3: Set up the proportion to find the required amount of shellac.
Using the unitary method, we can find the amount of shellac needed for 35 g of cement:
\[ \text{Required shellac} = \left( \frac{\text{mass of shellac}}{\text{total mass}} \right) \times \text{desired mass of cement} \]
\[ \text{Required shellac} = \left( \frac{12 \, \text{g}}{140 \, \text{g}} \right) \times 35 \, \text{g} \]

### Step 4: Calculate the required amount of shellac.
Now we perform the calculation:
\[ \text{Required shellac} = \left( \frac{12}{140} \right) \times 35 \]
\[ \text{Required shellac} = \frac{12 \times 35}{140} \]
\[ \text{Required shellac} = \frac{420}{140} = 3 \, \text{g} \]

### Conclusion
Thus, to make 35 g of benzene soluble cement, **3 g of shellac** should be taken.

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