SOLUTION: The middle digit of a three digit number is zero. The number is 34 times the sum of its digits. The new number obtained by interchaning the digits in the units and hundreds place i
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Question 984486: The middle digit of a three digit number is zero. The number is 34 times the sum of its digits. The new number obtained by interchaning the digits in the units and hundreds place is more than the original number by 395. Find the original number. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The middle digit of a three digit number is zero.
The number is 34 times the sum of its digits.
The new number obtained by interchanging the digits in the units and hundreds place is more than the original number by 395!!!!!
In order for this to work it has to be a multiple of 9, 396 would work
Find the original number.
:
let a = the 100's digit
let b = the 10's digit which we know is 0
let c = the units
:
The number is 34 times the sum of its digits.
100a + c = 34(a + c)
100a + c = 34a + 34c
100a - 34a = 34c - c
66a = 33c
simplify divide by 33
2a = c
:
"The new number obtained by interchaning the digits in the units and hundreds place is more than the original number by 396."
100c + a = 100a + c + 396
100c - c = 100a - a + 396
99c = 99a + 396
divide by 99
c = a + 4
Replace c with 2a
2a = a + 4
2a - a = 4
a = 4
then
c = 4 + 4
c = 8
:
Find the original number. It's 408
