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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 ? 

 Aug 2, 2016
 #1
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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

 Aug 2, 2016
 #2
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I assume the case is , is the decimal point.

 

4(38+x)26,729=209,4234(38+x)=236,15238+x=59,038x=21,038

 Aug 2, 2016

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