Question 96920: Three digit number. 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.
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Three digit number. 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.
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Let the number be 10^2h+10t+u
EQUATION:
h+t+u=11
The reverse of the number is 10^2u+10t+h
EQUATION:
10^2u+10t+h = 5(10^h+10t+u)+46
100u+10t+h = 500h+50t+5u+46
499h+40t-95u=-46
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EQUATION:
h+2t-u=0
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Rearranging the equations:
h t+ u=11
h+2t-u=0
499h+40t-95u=-46
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Using the Matrix function of a TI calculator
I get:
h=1 ; t=3; u=7
The number is 137
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Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! There is simple way to do the problem:
x = 100's, y = 10's, z = 1,s
:
From the phrase "5 times the old number" we know that the 1st number x = 1:
(5 times any other hundreds number would not be 3 digit number)
:
" The sum of the digits of a three-digit number is 11." therefore:
y + z = 10
:
" If the hundreds digit plus twice the tens digit is equal to the units digit,"
1 + 2y = z
y - z = -1
:
Add to the 1st equation
y + z = 10
2y- z = -1
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3y = 9
y = 3
:
Obviously z = 7
:
then what is the number. 137
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