Two-digit number with digit sum and digit difference A two-digit number has digits that sum to 14 and differ by 2. What is the product of the two digits of the number?

Introduction / Context:
Digit problems often give the sum and difference of two digits. This makes it straightforward to solve for the individual digits using simultaneous linear equations and then compute the desired product.

Given Data / Assumptions:

• Let the digits be L (larger) and S (smaller).
• L + S = 14.
• L − S = 2.
• We want L * S.

Concept / Approach:
Add and subtract the equations to isolate L and S. This is a standard method for two equations in two unknowns. After finding the digits, multiply them for the requested product.

Step-by-Step Solution:
Add equations: (L + S) + (L − S) = 14 + 2 → 2L = 16 → L = 8.Find S: S = 14 − L = 14 − 8 = 6.Product: L * S = 8 * 6 = 48.

Verification / Alternative check:
Digits 8 and 6 satisfy both conditions: sum 14, difference 2. The product 48 follows directly.

Why Other Options Are Wrong:
56 and 45 arise from mixing digits or arithmetic slips; 40 is another near miss; “Couldn't be determined” is incorrect because the system has a unique solution.

Common Pitfalls:
Interchanging sum and difference equations or assuming the digits can be in any order without checking the difference sign.

Final Answer:
48