The arithmetic mean of two numbers is 19, and their difference is 4. Find these numbers.

1) Since we are given the arithmetic mean of two numbers, which is 19, we write down the formula by which this value was calculated: a + b / 2 = 19.
2) Multiply by 2, and get rid of 2 in the denominator. a + b = 38
3) Since we are also given the difference a – b = 4, we can compose a system of equations:
a + b = 38;
a – b = 4; <=>
4 + b + b = 38;
a = 4 + b; <=>
2b = 38 – 4;
a = 4 + b; <=>
2b = 34;
a = 4 + b; <=>
b = 17;
a = 4 + 17; <=>
b = 17;
a = 21;
Let’s check: 17 + 21/2 = 19
21 – 17 = 4
Answer: a = 21; b = 17;