SOLUTION: The Sum of the digits of 3 digit number is 20. The middle digit is 1/4 of the sum of remaining two digits. If order of digits is reversed, the new number is more than earlier by 19

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Question 1066540: The Sum of the digits of 3 digit number is 20. The middle digit is 1/4 of the sum of remaining two digits. If order of digits is reversed, the new number is more than earlier by 198. Find original number.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
100h+10t+u, the original number

System of equations literally from the description:



system%28h%2Bt%2Bu=20%2C4t=h%2Bu%2C99u-99h=198%29
The first two equations of this revised system will quickly give you the tens placed digit: highlight%28t=4%29......

Substitute for t=4 and revise:

h%2Bu%2B4=20
h%2Bu=16
u%2Bh=16

system%2899u-99h=198%2Cu%2Bh=16%29
Multiply this second equation by 99:

system%2899u-99h=198%2C99u%2B99h=1584%29
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ADD corresponding members
198u=1782

highlight%28u=9%29

(Deleting earlier posted results....)

Answer by ikleyn(52779) About Me  (Show Source):