The sum of the two digits of a two-digit number is 14, and the difference…

Concept

For a two-digit number whose digits have a known sum S and a known difference D, each digit can be recovered by solving the linear system x + y = S and x − y = D: adding the two equations gives 2x = S + D, so x = (S + D) / 2, and subtracting gives 2y = S − D, so y = (S − D) / 2.

Application

1. Here S = 14 (the sum of the two digits) and D = 2 (the difference of the two digits).

2. Adding: 2x = 14 + 2 = 16, so x = 8.

3. Subtracting: 2y = 14 − 2 = 12, so y = 6.

4. The question asks for the product of the two digits: x × y = 8 × 6 = 48.

Cross-check

Verify both original conditions against the recovered digits: 8 + 6 = 14 (matches the given sum) and 8 − 6 = 2 (matches the given difference), so the digits are confirmed correct. Note that arranging these two digits as a two-digit number gives 86 or 68 — but the question asks for the product of the digits, not the two-digit number itself.

Result: The product of the two digits is 48.