one number is four more than twice another number. If both numbers are positive and the difference between the numbers is 27, determine the numbers.

Answer 1

Let x and y be the two numbers, both positive.

Assume x > y, because

x = 2y + 4 (1)

Also,

x - y = 27, that is

x = y + 27 (2)

Equate (1) and (2).

2y + 4 = y + 27

Subtract y from each side.

y + 4 = 27

Subtract 4 from each side.

y = 23

From (2), obtain

x = 23 + 27 = 50

Answer:

The two numbers are 50 and 23.