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Question 160793: The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number exceeds the original number by 198. Find the original number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number exceeds the original number by 198. Find the original number.
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Let x=100's digit; y=10's digit; z=units digit
:
"The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit."
The equation for this statement:
y - x = z - y
y + y = x + z
2y = x+z
;
"When the digits are reversed, the new number exceeds the original number by 198."
100z + 10y + x - (100x + 10z + z) = 198
100z + 10y + x - 100x - 10z - z = 198
100z - z + 10y - 10y + x - 100x = 198
99z - 99x = 198
Divide equation by 99:
z - x = 2
z = x + 2
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In the 1st equation substitute (x+2) for z
2y = x + (x+2)
2y = 2x + 2
Divide equation by 2
y = x + 2
x = y - 2
:
y has to > 2, (x can't = 0) try y = 3, use the two equations to find x and z
original number: 133, reverse number 331
331 - 133 = 198
:
Find the original number.
Here are some more numbers that will work
y=4; 442 - 244 = 198
y=5; 553 - 355 = 198
y=6; 664 - 466 = 198
y=7; 775 - 577 = 198
y=8; 886 - 688 = 198
y=9; 997 = 799 = 198
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