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3AB+C3D=7BD
The following addition example, each letter represents one digit. It’s the same letters represent the same digit, and different letters represent different digits, what digit does A represent?
1. Convert the equation into numerical form:
3AB + C3D = 7BD
2. Use the given information that each letter represents one digit:
Let A = x, B = y, C = z, D = w
3. Substitute the letters with the corresponding variables:
3xy + z3w = 7yw
4. Since B appears in both terms on the right side of the equation, we know that y must be less than or equal to 3 (as the maximum possible digit).
5. Now we can try different values for y (0, 1, 2, or 3) and solve for the other variables to see if the equation holds:
For y = 0:
3xy + z3w = 7yw
30 + 30z = 7w
30 + 30z = 7w is not possible, as both sides are multiples of 10.
For y = 1:
3x1 + z3w = 7w1
31 + z3w = 71
31 + z3w = 71 is not possible, as the right side is greater than 50.
For y = 2:
3x2 + z3w = 7w2
32 + z3w = 72
32 + z3w = 72 is not possible, as the left side is greater than 50.
For y = 3:
3x3 + z3w = 7w3
33 + z3w = 73
33 + z3w = 73 is possible when x = 4, z = 1, and w = 9.
Therefore, A = 4.