If A=3B = 5C, find A:B:C.

Answer

To solve the problem where \( A = 3B = 5C \) and we need to find the ratio \( A:B:C \), we can follow these steps:

### Step 1: Set up the equations
We start with the given relationships:
\[ A = 3B \quad \text{and} \quad A = 5C \]

### Step 2: Express B and C in terms of A
From \( A = 3B \), we can express \( B \) in terms of \( A \):
\[ B = \frac{A}{3} \]
From \( A = 5C \), we can express \( C \) in terms of \( A \):
\[ C = \frac{A}{5} \]

### Step 3: Find a common multiple for B and C
To find the ratio \( A:B:C \), we need to express \( B \) and \( C \) using a common multiple. The least common multiple (LCM) of the denominators (3 and 5) is 15.

### Step 4: Express A, B, and C using the LCM
Now we can express \( A \), \( B \), and \( C \) in terms of the common multiple:
\[ A = A \quad (as \, it \, is) \]
\[ B = \frac{A}{3} = \frac{A \times 5}{15} = \frac{5A}{15} \]
\[ C = \frac{A}{5} = \frac{A \times 3}{15} = \frac{3A}{15} \]

### Step 5: Write the ratios
Now we can write the ratios:
\[ A:B:C = A : \frac{5A}{15} : \frac{3A}{15} \]
To simplify, we can factor out \( A \):
\[ A:B:C = 1 : \frac{5}{15} : \frac{3}{15} \]
This simplifies to:
\[ A:B:C = 1 : \frac{1}{3} : \frac{1}{5} \]

### Step 6: Convert to whole numbers
To express this in whole numbers, we can multiply each part of the ratio by 15 (the LCM):
\[ A:B:C = 15 : 5 : 3 \]

### Final Answer
Thus, the ratio \( A:B:C \) is:
\[ \boxed{15:5:3} \]