The sum of two numbers is 53. If twice the smaller is subtracted from the larger number, the result is 17. Find the two numbers.

Let the two numbers be L and
S.

The sum of the two numbers is
53

L + S = 53 ...(1)

Twice the
smaller number subtracted from the larger number gives
17.

L - 2S = 17 ...(2)

(1) -
(2)

=> L + S - L + 2S = 53 -
17

=> 3S = 36

=>
S = 12

L = 53 - S = 53 - 12 =
41

The smaller number is 12 and the larger
number is 41.