Three-digit - sum

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.

Final 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  Row2901 Row1Row2 2b+c=12  Pivot:Row2Row3  Row392 Row2Row3 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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