38 is added to a mystery number. The result is multiplied by 4. After that 26,729 is then subtracted . The final value is 209,423. What was the mystery number at the beginning ?
Let the mystery number =N
{[N+38] x 4 - 26,729} =209,423
Solve for N:
4 (N+38)-26729 = 209423
4 (N+38) = 4 N+152:
4 N+152-26729 = 209423
Add like terms. 152-26729 = -26577:
4 N-26577 = 209423
Add 26577 to both sides:
4 N+(26577-26577) = 209423+26577
26577-26577 = 0:
4 N = 209423+26577
209423+26577 = 236000:
4 N = 236000
Divide both sides of 4 N = 236000 by 4:
(4 N)/4 = 236000/4
4/4 = 1:
N = 236000/4
The gcd of 236000 and 4 is 4, so 236000/4 = (4×59000)/(4×1) = 4/4×59000 = 59000:
Answer: |N = 59,000
