Three-digit 81064

A three-digit number has a digit sum of 16. If we change the digits in the hundreds and tens places in this number, the number is reduced by 360. If we swap the ten's and one's digits in the original number, the number increases by 54. Find this three-digit number.

Correct answer:

x =  628

Step-by-step explanation:

A+B+C=16 ABCBAC=360 ACBABC=54  6+2+8=16 628268=360 682628=54  x=628   Verifying Solution:   a+b+c=16 a 100+b 10+c(b 100+a 10+c)=360 (a 100+c 10+b)(a 100+b 10+c)=54  a+b+c=16 90a90b=360 9b9c=54  Pivot:Row1Row2 90a90b=360 a+b+c=16 9b9c=54  Row2901 Row1Row2 90a90b=360 2b+c=12 9b9c=54  Pivot:Row2Row3 90a90b=360 9b9c=54 2b+c=12  Row392 Row2Row3 90a90b=360 9b9c=54 3c=24  c=324=8 b=954+9c=954+9 8=2 a=90360+90b=90360+90 2=6  a=6 b=2 c=8  X=a 100+b 10+c=6 100+2 10+8=628

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