The sum of the digits of a two-digit number is 15 and their difference is 3. What is the two-digit number?

Problem restatement
Let the tens digit be a and the units digit be b. Given a + b = 15 and a − b = 3, find the number 10a + b.

Given data

• a + b = 15
• a − b = 3

Concept/Approach
Solve the simultaneous linear equations.

Step-by-step calculation
Add the equations: (a + b) + (a − b) = 15 + 3 2a = 18 → a = 9 Then b = 15 − 9 = 6 Number = 10a + b = 10×9 + 6 = 96

Verification/Alternative
Digits 9 and 6 have sum 15 and difference 3; number 96 fits.

Common pitfalls

• Taking 69 instead of 96; the equations make tens digit 9, units 6.

Final Answer
96