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

Options

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

Answer

To solve the equation \( \frac{3 \frac{7}{a} \times b \frac{3}{15}}{8} = 1 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ \frac{3 \frac{7}{a} \times b \frac{3}{15}}{8} = 1 \]
This can be rewritten as:
\[ 3 \frac{7}{a} \times b \frac{3}{15} = 8 \]

### Step 2: Simplify the fractions
We can express the fractions in a more manageable way. The term \( b \frac{3}{15} \) simplifies to \( \frac{b}{5} \):
\[ 3 \frac{7}{a} \times \frac{b}{5} = 8 \]

### Step 3: Combine the terms
Now, we can combine the terms:
\[ \frac{21b}{5a} = 8 \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 21b = 40a \]

### Step 5: Express \( b \) in terms of \( a \)
From the equation \( 21b = 40a \), we can express \( b \) as:
\[ b = \frac{40a}{21} \]

### Step 6: Determine the values of \( a \) and \( b \)
To find suitable integer values for \( a \) and \( b \), we need \( a \) to be greater than 7 (since \( \frac{7}{a} \) must be a proper fraction). The smallest integer greater than 7 is 11.

Let's substitute \( a = 11 \):
\[ b = \frac{40 \times 11}{21} = \frac{440}{21} \approx 20.95 \]
Since \( b \) must also be an integer, we try the next integer \( a = 15 \):
\[ b = \frac{40 \times 15}{21} = \frac{600}{21} \approx 28.57 \]
This also does not yield an integer.

Next, we try \( a = 21 \):
\[ b = \frac{40 \times 21}{21} = 40 \]
This gives us integer values \( a = 21 \) and \( b = 40 \).

### Final Result
Thus, the values of \( a \) and \( b \) are:
\[ a = 21, \quad b = 40 \]