In the addition problem find the digit represented by C. Each time a letter appears it represent the same digit. A does not equal 0 (zero).
AB
AB
AB
+ AB
______
CA
please explain your results
Thanks
since 4B = A with a carry,
B > 2 and A is a multiple of 4.
Since 4A plus the carry generates no carry, 4A < 9 or A <= 2
So, I'd say A=2 and B can be 3 or 8, but 4*28 is 3 digits, so we have
23+23+23+23 = 92
Aba
+bab
---------
Ccc
All posible values for all
RNFNF
To find the value represented by the letter C in the addition problem, we need to solve the given equation:
AB + AB + AB + AB = CA
In this equation, A and B represent digits, and we need to find the value of C.
Let's break down the process of solving this problem step-by-step:
Step 1: Start with the least significant digit (the rightmost digit) of the equation. In this case, it is A.
Step 2: Notice that A appears four times on the left side of the equation, so the value of A must be four times the value of itself. Therefore, A must be 0 (zero) since it is the only digit that multiplied by four equals itself (0 x 4 = 0).
Step 3: Now that we know A is 0, we can rewrite the equation as follows:
0B + 0B + 0B + 0B = C0
Step 4: Since there are no other digits to add, we can see that the sum of the ones place (B + B + B + B) should equal 10 + C. In other words:
4B = 10 + C
Step 5: To solve for B, we can isolate the variable B by subtracting 10 from both sides of the equation:
4B - 10 = C
Step 6: Now, let's find the values that satisfy this equation. We know that B must be a digit between 0 and 9, inclusive, so we can simply try out different values of B and see if any of them satisfy the equation.
Starting with B = 0:
4(0) - 10 = -10 ≠ C
Trying B = 1:
4(1) - 10 = -6 ≠ C
Trying B = 2:
4(2) - 10 = -2 ≠ C
Trying B = 3:
4(3) - 10 = 2 ≠ C
Trying B = 4:
4(4) - 10 = 6 ≠ C
Trying B = 5:
4(5) - 10 = 10 = C
Step 7: From our calculations, we find that when B = 5, C = 10 satisfies the equation. Therefore, the digit represented by C is 1.
The final answer is that the digit represented by C is 1.
I hope this explanation helps you understand how to solve this addition problem!