AB+CD=AAA
What is the value of C?
Choices: 1, 3, 7, 9, or N/A
Easier if you write it as
_AB
_CD+
____
AAA
The largest A+C can be is 18 (1 carried plus say A or C=9 and A or C=8) so A must =1 (it can't=0)
re-write
_1B
_CD+
____
111
In order for 1+C=11, C =9 with 1 carried from B+D.
We don't need to know what B and D are.
To find the value of C in the equation AB + CD = AAA, we need to follow a step-by-step process.
1. We know that A and B are digits, and C and D are also digits.
2. The equation states that AB + CD = AAA, which means that the sum of AB and CD is equal to AAA.
3. Since AAA is a three-digit number, A must be greater than or equal to 1 and less than or equal to 9 (excluding 0).
4. We need to consider all possible values of A and find the corresponding values of B, C, and D that satisfy the equation.
5. We can start by assuming a value for A, say A = 1.
- For A = 1, the equation becomes 1B + CD = 111.
- Since B and D are digits, their sum B + D cannot be greater than 9.
- The only combination of two-digit numbers B + D that gives a three-digit sum equal to or greater than 111 is 99. This means B + D = 99.
- Since B + D = 99, and B and D are digits, B must be 9 and D must be 9.
- Therefore, the equation becomes 19 + C9 = 111.
- To solve for C, we can subtract 19 from both sides of the equation: C9 = 111 - 19.
- Simplifying, we get C9 = 92.
- From this equation, we can see that C = 9.
6. Continuing this process for all possible values of A, we can evaluate the equation and find the corresponding values of C.
By going through all possible values of A, it is clear that the only possible value for C is 9. Thus, the value of C is 9.