SOLUTION: The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more that five the old number. If the hundreds digit plus twice the tens dig

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Question 167005: The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more that five the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number,
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I am going to re-write the problem to what I think you meant:
:
The sum of the digits of a three-digit number is 11. If the digits are reversed,
the new number is 46 more than five times the old number. If the hundreds digit
plus twice the tens digit is equal to the units digit, then what is the number,
:
Let the number be: 100x + 10y + z
:
Let's try solving this using only the 1st and last statements:
"The sum of the digits of a three-digit number is 11."
x + y + z = 11
:
"the hundreds digit plus twice the tens digit is equal to the units digit,"
x + 2y = z
x + 2y - z = 0
:
Add to the 1st equation to eliminate z
x + y + z = 11
x +2y - z = 0
--------------
2x + 3y = 11
:
2x = 11 - 3y
x = %28%2811-3y%29%29%2F2
Only two values for y will give a positive integer value for x, namely 1 and 3:
From the 2nd statement we know that x is a low value, therefore 3 seems likely:
x = %28%2811-3%283%29%29%29%2F2
x = %28%2811-9%29%29%2F2
x = 2%2F2
x = 1 when y = 3
Find z
1 + 3 + z = 11
z = 11-4
z = 7
;
Our number is 137
:
See if that makes the 2nd statement true.
"If the digits are reversed, the new number is 46 more than five times the old number"
731 = 5(137) + 46
731 = 685 + 46