If a, b, and c are digits for which
7 a 2
-4 8 b
=========
c 7 3
then a + b + b = _______
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
To solve this problem, we need to perform the subtraction given in the equation and find the values of a, b, and c.
Let's start by subtracting the bottom row from the top two rows individually:
From the units place, we have:
2 - b = 3 (carry over is 0)
Next, let's subtract the tens place:
8 - 4 = 4 (carry over is 0)
Finally, let's subtract the hundreds place:
7 - a = c (carry over is 0)
Now, let's analyze the given information:
From the units place:
2 - b = 3
By subtracting 2 from both sides, we have:
-b = 1
Multiply both sides by -1 to isolate b:
b = -1
From the tens place:
8 - 4 = 4
This equation is true, and it doesn't provide us with any additional information.
From the hundreds place:
7 - a = c
By subtracting 7 from both sides, we have:
-a = c - 7
Multiply both sides by -1 to isolate a:
a = -c + 7
Based on the given options, a, b, and c must be digits, which indicates that they must be positive integers. Since b = -1, this violates the condition of being a digit. Therefore, such a solution is not possible.
Therefore, there is no valid solution for a + b + b, and the answer is not among the given options.