SOLUTION: A three digit number is equal to 17 times the sums of the digits . If 198 is added to the number, the extreme digits get interchanged . The sums of the first and third digits is 1

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Question 1067202: A three digit number is equal to 17 times the sums of the digits . If 198 is added to the number, the extreme digits get interchanged . The sums of the first and third digits is 1 less than the middle digit. Find the number.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
t,h,u, for tens hundreds ones

100h%2B10t%2Bu, the number



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100h%2B10t%2Bu-17h-17t-17u=0
83h-7t-16u=0
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100h%2B10t%2Bu-h-10t-100u%2B198=0
99h-99u=-198
h-u=-2
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h%2Bu-t=-1


Revised system of equations: system%2883h-7t-16u=0%2Ch-u=-2%2Ch%2Bu-t=-1%29

Substitute using t=h+u+1 into the first equation.
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83h-7%28h%2Bu%2B1%29-16u=0
83h-7h-7u-7-16u=0
76h-23u=7
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Simpler system in two variables, system%2876h-23u=7%2Cu-h=2%29

76h-23u%2B%2823u-23h%29=7%2B46
76h-23h=53
53h=53
highlight%28h=1%29-------the Hundreds place


Again using the simpler system
u-h=2
u=2%2Bh
u=2%2B1
highlight%28u=3%29--------the Ones place


Returning to the Revised System equation of t=h+u+1
t=1%2B3%2B1
highlight%28t=5%29


The three digit number is 153.