Answer:
The original number is 245.
Step-by-step explanation:
Let A be the hundreds digit of the original number, B be the tens digit of the original number, and C be the units digit of the original number.
We know from the first two sentences in the problem that:
C = 5
A + B + C = 11
Substituting the value of C, we get:
A + B + 5 = 11
A + B = 6
In the third sentence, we are told that when the number is added to the reverse of itself, the sum of the two numbers is 787. Expressed mathematically:
100A + 10B + C + A + 10B + 100C = 787
Where (100A + 10B + C) gives the value of the original number and (A + 10B + 100C) gives the value of the number when reversed. Simplified, we get:
101A + 20B + 101C = 787
Rewriting the "A + B = 6" equation from above as B = 6 - A, we substitute (6 - A) into the equation above for B and substitute 5 for C (because we know C = 5):
101A + 20(6 - A) + 101 * 5 = 787
101A + 120 - 20A + 505 = 787
81A + 625 = 787
81A = 162
A = 2
Now that we have A, we can get B using A + B = 6:
2 + B = 6
B = 4
To summarize:
A = 2
B = 4
C = 5
So the original number must be 245.
