If `a:b=3:2` and `b:C=6:5` then `a:b:c` is equal to

Options

A. `9:6:5`
B. `9:6:10`
C. `3:3:5`
D. `3:6:5`

Answer

To find the combined ratio \( a:b:c \) given \( a:b = 3:2 \) and \( b:c = 6:5 \), we can follow these steps:

### Step 1: Express the Ratios
We start with the given ratios:
- \( a:b = 3:2 \)
- \( b:c = 6:5 \)

### Step 2: Equalize the Common Term (b)
The common term in both ratios is \( b \). In the first ratio, \( b \) is represented as 2, and in the second ratio, it is represented as 6. To combine these ratios, we need to make the values of \( b \) the same.

To do this, we can find a common multiple of 2 and 6. The least common multiple (LCM) of 2 and 6 is 6.

### Step 3: Scale the First Ratio
We need to scale the first ratio \( a:b = 3:2 \) so that \( b = 6 \). We can do this by multiplying both parts of the ratio by 3:
\[ a:b = 3 \times 3 : 2 \times 3 = 9:6 \]

### Step 4: Use the Second Ratio
Now we can use the second ratio \( b:c = 6:5 \) directly since \( b \) is already 6:
\[ b:c = 6:5 \]

### Step 5: Combine the Ratios
Now we have:
- \( a:b = 9:6 \)
- \( b:c = 6:5 \)

We can now combine these ratios:
\[ a:b:c = 9:6:5 \]

### Final Answer
Thus, the combined ratio \( a:b:c \) is:
\[ \boxed{9:6:5} \]