If `R:S = 3:1 and S:T = 1:5`, then `R:S:T=` _________.

Answer

To solve the problem of finding the combined ratio \( R:S:T \) given \( R:S = 3:1 \) and \( S:T = 1:5 \), we can follow these steps:

### Step 1: Write down the given ratios
We have:
- \( R:S = 3:1 \)
- \( S:T = 1:5 \)

### Step 2: Express the ratios in terms of a common variable
From the first ratio \( R:S = 3:1 \), we can express:
- \( R = 3x \)
- \( S = 1x \) (where \( x \) is a common multiplier)

From the second ratio \( S:T = 1:5 \), we can express:
- \( S = 1y \)
- \( T = 5y \) (where \( y \) is another common multiplier)

### Step 3: Set the expressions for S equal to each other
Since both expressions represent \( S \), we can set them equal:
\[ 1x = 1y \]
This implies:
\[ x = y \]

### Step 4: Substitute back to find R and T in terms of x
Now we can substitute \( y \) with \( x \):
- \( S = 1x \)
- \( T = 5y = 5x \)

Now we have:
- \( R = 3x \)
- \( S = 1x \)
- \( T = 5x \)

### Step 5: Write the combined ratio
Now we can express the combined ratio \( R:S:T \):
\[ R:S:T = 3x : 1x : 5x \]

### Step 6: Simplify the ratio
Since \( x \) is a common factor, we can simplify the ratio:
\[ R:S:T = 3 : 1 : 5 \]

### Final Answer
Thus, the combined ratio \( R:S:T \) is:
\[ R:S:T = 3:1:5 \]

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