SOLUTION: I need to set up three algebraic equations in order to solve this problem. Here is the word problem that I have: "The sum of the digits of a certain three digit number is nine.

Algebra ->  Matrices-and-determiminant -> SOLUTION: I need to set up three algebraic equations in order to solve this problem. Here is the word problem that I have: "The sum of the digits of a certain three digit number is nine.      Log On


   

Question 383355: I need to set up three algebraic equations in order to solve this problem. Here is the word problem that I have:
"The sum of the digits of a certain three digit number is nine. The sum of the hundreds and tens digits is equal to the ones digit minus one. The number, divided by nine, equals three times the ones digit. What is the number?"
So far, I have:
x + y + z = 9
x + y - z = -1 (Originally x + y = z - 1)
I can't figure out the third one. Help please!

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: "The number, divided by nine, equals three times the ones digit" means that %28100x%2B10y%2Bz%29%2F9=3z


If you multiply both sides by 9, you get 100x%2B10y%2Bz=27z

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
"The sum of the digits of a certain three digit number is nine.
The sum of the hundreds and tens digits is equal to the ones digit minus one. The number, divided by nine, equals three times the ones digit. What is the number?"
===========================
h + t + u = 9
h + t = u-1
(100h + 10t + u)/9 = 3u
------------------------------
Rearrange:
h + t + u = 9
h + t - u = -1
100h+ 10t -26u = 0
---------------------------
Solve using any method you know to get:
h = 1
t = 3
u = 5
=============
The number is 135
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Cheers,
Stan H.