The value of a and b in `3 (7)/axxb(3)/15 = 8` is equal to

Options

A. `2,11`
B. `11,2`
C. `1,1`
D. `2,1`

Answer

To solve the equation \( \frac{3 \cdot \frac{7}{a} \cdot \frac{b}{3}}{15} = 8 \), we will follow these steps:

### Step 1: Simplify the Equation
Start by simplifying the left-hand side of the equation:
\[ \frac{3 \cdot \frac{7}{a} \cdot \frac{b}{3}}{15} = \frac{7b}{15a} \]
So, we rewrite the equation as:
\[ \frac{7b}{15a} = 8 \]

### Step 2: Cross-Multiply
Cross-multiply to eliminate the fraction:
\[ 7b = 8 \cdot 15a \]
This simplifies to:
\[ 7b = 120a \]

### Step 3: Express b in Terms of a
Now, we can express \( b \) in terms of \( a \):
\[ b = \frac{120a}{7} \]

### Step 4: Find Suitable Values for a and b
Since \( a \) and \( b \) must be integers, we need \( 120a \) to be divisible by \( 7 \). We can check the options given (211, 11, 211, or 21) to find suitable values.

1. **Option 1: \( a = 11 \)**
\[ b = \frac{120 \cdot 11}{7} = \frac{1320}{7} = 188.57 \quad (\text{not an integer}) \]

2. **Option 2: \( a = 21 \)**
\[ b = \frac{120 \cdot 21}{7} = \frac{2520}{7} = 360 \quad (\text{is an integer}) \]

### Step 5: Verify the Solution
Now, we can verify if \( a = 21 \) and \( b = 360 \) satisfy the original equation:
\[ \frac{3 \cdot \frac{7}{21} \cdot \frac{360}{3}}{15} = \frac{3 \cdot \frac{7}{21} \cdot 120}{15} \]
This simplifies to:
\[ \frac{3 \cdot \frac{7 \cdot 120}{21 \cdot 15}} = \frac{3 \cdot 7 \cdot 8}{21} = \frac{168}{21} = 8 \]

Thus, the values of \( a \) and \( b \) are:
\[ a = 21, \quad b = 360 \]

### Final Answer
The values of \( a \) and \( b \) are \( 21 \) and \( 360 \) respectively.

---