SOLUTION: the sum of the digits of a three-digit number is 17. if the digits are reversed and the resulting number is added to the original number, the result is 1474. if the resulting numbe

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: the sum of the digits of a three-digit number is 17. if the digits are reversed and the resulting number is added to the original number, the result is 1474. if the resulting numbe      Log On

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Question 1037154: the sum of the digits of a three-digit number is 17. if the digits are reversed and the resulting number is added to the original number, the result is 1474. if the resulting number is subtracted from the original number, the result is 396. find the original number
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
t, the tens digit
h, the hundreds digit
u, the ONES or units digit

This system fits the description:


SIMPLIFY
system%28t%2Bh%2Bu=17%2C101u%2B20t%2B101h=1474%2C99u-99h=396%29
system%28t%2Bh%2Bu=17%2C20t%2B101h%2B101u=1474%2C-11h%2B11u=44%29
system%28t%2Bh%2Bu=17%2C20t%2B101h%2B101u=1474%2C-h%2Bu=4%29


SOLVE THE SYSTEM
Neat way to solve the system could be use first two equations to eliminate t.
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system%2820t%2B20h%2B20u=340%2C20t%2B101h%2B101u=1474%2C-h%2Bu=4%29
system%2881h%2B81u=1134%2C-h%2Bu=4%29
system%28h%2Bu=14%2C-h%2Bu=4%29
Use very simple Elimination, add corresponding members...
2u=18
highlight%28u=9%29------found ONES digit.
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h%2Bu=14
h=14-u
h=14-9
highlight%28h=5%29-------HUNDREDS digit found.
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Return to h%2Bt%2Bu=17;
t=17-h-u
t=17-5-9
t=17-14
highlight%28t=3%29
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-
Original Number: 539

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

the sum of the digits of a three-digit number is 17. if the digits are reversed and the resulting number is added to the original number, the result is 1474. if the resulting number is subtracted from the original number, the result is 396. find the original number
Original number: highlight_green%28935%29