Gold is 19 times heavier than water. Copper is 9 times heavier than water. In which ratio gold and copper should be mixed so that mixture is 15 times heavier than water ?

Answer

To solve the problem of mixing gold and copper so that the mixture is 15 times heavier than water, we can follow these steps:

### Step 1: Define the weights of gold and copper in terms of water.
- Let the weight of water be \( W \).
- The weight of gold, which is 19 times heavier than water, will be \( 19W \).
- The weight of copper, which is 9 times heavier than water, will be \( 9W \).

### Step 2: Define the weight of the desired mixture.
- The weight of the mixture should be 15 times heavier than water, which is \( 15W \).

### Step 3: Set up the allegation method.
- We will use the allegation method to find the ratio in which gold and copper should be mixed.
- The weights are as follows:
- Gold: \( 19W \)
- Copper: \( 9W \)
- Mixture: \( 15W \)

### Step 4: Calculate the differences using the allegation method.
- The difference between the weight of gold and the weight of the mixture:
\[ 19W - 15W = 4W \]
- The difference between the weight of copper and the weight of the mixture:
\[ 15W - 9W = 6W \]

### Step 5: Establish the ratio of gold to copper.
- The ratio of gold to copper can be expressed as:
\[ \text{Ratio of Gold to Copper} = \frac{6W}{4W} = \frac{6}{4} = \frac{3}{2} \]

### Conclusion:
- Therefore, gold and copper should be mixed in the ratio of \( 3:2 \).

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