If 4A = 5B = 8C, then A : B : C is:

Options

A. `10:8:5`
B. `12:8:7`
C. `12:7:5`
D. `10:8:7`

Answer

To solve the problem where \( 4A = 5B = 8C \), we need to express \( A \), \( B \), and \( C \) in terms of a common variable. Let's go through the steps:

### Step 1: Set a common variable
Let \( k \) be the common value such that:
\[ 4A = 5B = 8C = k \]

### Step 2: Express \( A \), \( B \), and \( C \) in terms of \( k \)
From the equation \( 4A = k \):
\[ A = \frac{k}{4} \]

From the equation \( 5B = k \):
\[ B = \frac{k}{5} \]

From the equation \( 8C = k \):
\[ C = \frac{k}{8} \]

### Step 3: Write the ratios \( A : B : C \)
Now we can express the ratio \( A : B : C \):
\[ A : B : C = \frac{k}{4} : \frac{k}{5} : \frac{k}{8} \]

### Step 4: Eliminate \( k \) from the ratio
To eliminate \( k \), we can multiply each term by the least common multiple (LCM) of the denominators (4, 5, and 8). The LCM of 4, 5, and 8 is 40. Thus, we multiply each term by 40:
\[ A : B : C = 40 \cdot \frac{k}{4} : 40 \cdot \frac{k}{5} : 40 \cdot \frac{k}{8} \]
This simplifies to:
\[ A : B : C = 10k : 8k : 5k \]

### Step 5: Simplify the ratio
Now we can simplify the ratio by removing \( k \):
\[ A : B : C = 10 : 8 : 5 \]

### Final Answer
Thus, the ratio \( A : B : C \) is:
\[ \boxed{10 : 8 : 5} \]