SOLUTION: a 4 digit postitive integer such that the sum of the digits is 18 & my digits reversed are exactly 4 times greater than myself. What number is it?

Question 211802: a 4 digit postitive integer such that the sum of the digits is 18 & my digits reversed are exactly 4 times greater than myself. What number is it?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a four-digit positive integer such that the sum of the digits is 18 & my digits
reversed are exactly four times greater than myself. What number is it?
:
We know the 1st digit has to be 1 or 2, (multiplying any other number by 4
would give us a 5 digit number)
:
Assuming it's 2, then the last digit of the number would be 8 (4*2=8); the 1st digit of the reversed number
:
let the middle digits be x & y:
:
2 + x + y + 8 = 18
x + y = 18 - 10
x + y = 8
:
2000 + 100x + 10y + 8 = the number
:
"digits reversed are exactly four times greater than myself.
4(2000 + 100x + 10y + 8) = 8000 + 100y + 10x + 2
:
8000 + 400x + 40y + 32 = 8000 + 100y + 10x + 2
;
400x + 40y + 8032 = 100y + 10x + 8002
400x - 10x + 40y - 100y = 8002 - 8032
390x - 60y = - 30
:
Simplify, divide by 10
39x - 6y = -3
:
Multiply the 1st equation (x + y = 8) by 6 and add
39x - 6y = -3
6x + 6y = 48
-------------- adding eliminates y
45x = 45
x = 1 is the 2nd digit
then, obviously since x + y = 8:
y = 7 is the 3rd digit
:
2178 is the number
:
4 * 2178 = 8712; the reversed number
RELATED QUESTIONS
I am a four-digit positive integer such that the sum of my digits is 18 and my digits... (answered by ankor@dixie-net.com)

Find a 2 digit Number such that 4 times the unit digit is 5 greater than thrice the ten... (answered by solver91311)

4 times the sum of the digits of a 2 digit number is equal to the number.If the digits... (answered by ankor@dixie-net.com)

I am a 4 digit number greater than 9,000. My hundreds digit is twice my ones digit. (answered by richard1234)

A two digit number is 4 times the sum of its digits. If 27 is added to that number its... (answered by josmiceli)

A two digit number such that its tens digit is greater than its unit digits by 4. The two (answered by josgarithmetic)

a two digit number such that its tens digit is greater than its unit digits by 4.the two... (answered by solver91311)

A number is made up of two digits such that 3 times the unit digit exceeds the tens digit (answered by Alan3354)

I am a 4 digit number. My thousands digit is the sum of my tens digit and ones digit. My... (answered by Edwin McCravy)