Find the triplicate ratio of 7 : 5.

Options

A. `125 : 343`
B. `343 : 125`
C. `344 : 125`
D. `343 : 126`

Answer

To find the triplicate ratio of 7 : 5, we follow these steps:

### Step 1: Understand the concept of triplicate ratio
The triplicate ratio of two numbers \( a : b \) is found by cubing both numbers. This means we will raise both numbers to the power of 3.

### Step 2: Cube the numbers
For the ratio 7 : 5, we will calculate:
- \( 7^3 \)
- \( 5^3 \)

### Step 3: Calculate \( 7^3 \)
\[ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343 \]

### Step 4: Calculate \( 5^3 \)
\[ 5^3 = 5 \times 5 \times 5 = 25 \times 5 = 125 \]

### Step 5: Write the triplicate ratio
Now we can write the triplicate ratio of 7 : 5 as:
\[ 343 : 125 \]

### Final Answer
The triplicate ratio of 7 : 5 is \( 343 : 125 \).

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