Gold is 19 times as heavy as water and copper is 9 times as heavy as water, in what ratio should these be mixed to get an alloy 15 times as heavy as water?

Options

A. `1:1`
B. `1:2`
C. `2:3`
D. `3:2`

Answer

To solve the problem of mixing gold and copper to create an alloy that is 15 times as heavy as water, we can follow these steps:

### Step 1: Define the weights of gold and copper in terms of water
- Gold is 19 times as heavy as water.
- Copper is 9 times as heavy as water.

### Step 2: Set up the equation for the mixture
Let the ratio of gold to copper be \( x:y \). The weight of the mixture can be expressed as:
\[ \text{Weight of mixture} = 19x + 9y \]
We want this mixture to be 15 times as heavy as water, so we set up the equation:
\[ 19x + 9y = 15(x + y) \]

### Step 3: Simplify the equation
Expanding the right side gives:
\[ 19x + 9y = 15x + 15y \]
Now, rearranging the terms, we get:
\[ 19x - 15x = 15y - 9y \]
This simplifies to:
\[ 4x = 6y \]

### Step 4: Solve for the ratio of gold to copper
Dividing both sides by 2 gives:
\[ 2x = 3y \]
Thus, the ratio \( \frac{x}{y} \) can be expressed as:
\[ \frac{x}{y} = \frac{3}{2} \]

### Step 5: Write the final ratio
This means the ratio of gold to copper should be 3:2.

### Conclusion
The final ratio in which gold and copper should be mixed to obtain an alloy that is 15 times as heavy as water is **3:2**.

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