The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers?

let x be the larger of the two numbers, and y be the other number.

Then:

x + y = 20   ...   (1)

and

x = 2y - 4

Shifting the term 2y in above equation from right to left hand side we get:

x - 2y = -4   ...   (2)

Subtracting equation (2) from equation (1) we get:

x - x + y + 2y = 20 + 4

3y = 24

Therefore:

y = 24/3 = 8

Substituting this value of y in equation (1) we get:

x + 8 = 20

x = 20 - 8 = 12

Answer:

Two numbers are 12 and 8.