Find the values of A and B in the following
`({:(," "4A),(,xx6):})/(" "2B4)`

Options

A. 4,6
B. 6,4
C. 4,4
D. 6,6

Answer

To solve the problem and find the values of A and B in the expression `({:(," "4A),(,xx6):})/(" "2B4)`, we can break it down step by step.

### Step 1: Understand the equation
We have the expression `4A * 6 = 2B4`. Here, `4A` means 4 followed by the digit A, and `2B4` means 2 followed by the digit B followed by 4.

### Step 2: Rewrite the numbers
We can express `4A` and `2B4` in terms of A and B:
- `4A` can be expressed as \( 40 + A \)
- `2B4` can be expressed as \( 200 + 10B + 4 \)

### Step 3: Set up the equation
Now, we can set up the equation based on the expression:
\[ (40 + A) \times 6 = 200 + 10B + 4 \]

### Step 4: Simplify the left side
Calculating the left side:
\[ (40 + A) \times 6 = 240 + 6A \]

### Step 5: Set the equation
Now we have:
\[ 240 + 6A = 204 + 10B \]

### Step 6: Rearranging the equation
Rearranging gives us:
\[ 6A - 10B = 204 - 240 \]
\[ 6A - 10B = -36 \]

### Step 7: Simplify the equation
Dividing the entire equation by 2:
\[ 3A - 5B = -18 \]

### Step 8: Find integer solutions
Now we need to find integer values for A and B. Since A and B are digits (0-9), we can test values for A to find corresponding B.

1. If \( A = 4 \):
\[ 3(4) - 5B = -18 \implies 12 - 5B = -18 \implies -5B = -30 \implies B = 6 \]

### Step 9: Verify the values
Now we have \( A = 4 \) and \( B = 6 \). Let's verify:
- \( 4A = 44 \)
- \( 2B4 = 264 \)

Calculating:
\[ 44 \times 6 = 264 \]
This confirms our values are correct.

### Final Answer:
The values are \( A = 4 \) and \( B = 6 \).

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