Question

In the addition problem below, the numbers being

added have unknown digits signified by the letters
"A" and "B". Assume that the unknown digits named
by the same letter are the same digit. Determine
which of the following choices best describes the
relationship of missing digits. 1ABA+32B = 2205

A. B-A=1
B. A + B = 15
C. A-B=2
D. A = B

Answer 1

The correct choice that describes the relationship of the missing digits is:

A = B. The correct answer is option D.

To determine the relationship of the missing digits in the equation 1ABA + 32B = 2205, let's break down the equation step by step.

First, let's focus on the units place. In the given equation, the units place of the left-hand side (LHS) is A, while the units place of the right-hand side (RHS) is 5. For the sum to be equal, A + B should result in a number that ends with 5.

Since B can only be a single digit, A + B cannot be greater than 9. This means A + B can only equal 5 or 15 (since adding the carry-over from the tens place to 5 gives us 15).

Next, let's move to the tens place. In the given equation, the tens place of the LHS is B, while the tens place of the RHS is 2. For the sum to be equal, B should be 2.

Now, let's look at the hundreds place. In the given equation, the hundreds place of the LHS is B, while the hundreds place of the RHS is 2. Since we already determined that B is 2, the hundreds place is consistent.

Finally, let's consider the thousands place. In the given equation, the thousands place of the LHS is 1, while the thousands place of the RHS is 2. This means A is 2.

Based on these deductions, we can conclude that the relationship of the missing digits is:

A = 2 and B = 2

Therefore, the correct choice that describes the relationship of the missing digits is:

D. A = B