SOLUTION: The sum of a hundreds digit and the tens digit of a three digit number is 13. If the hundreds digit and the tens digit are interchanged, the new number is 90 less than the original

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Question 937783: The sum of a hundreds digit and the tens digit of a three digit number is 13. If the hundreds digit and the tens digit are interchanged, the new number is 90 less than the original number. It is given that the units digit of the original number is 4. Find the original number.
plz solve this question my simultaneous equations. Substitution or Elimination.
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Original number 100h%2B10t%2Bu.
u=4;
h%2Bt=13;
100t%2B10h%2Bu=-90%2B100h%2B10t%2Bu----The digit interchange description.

Solve for the two variables, t and h.
(u is given already).

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of a hundreds digit and the tens digit of a three digit number is 13. If the hundreds digit and the tens digit are interchanged, the new number is 90 less than the original number. It is given that the units digit of the original number is 4. Find the original number.
***
let u=units digit
let t=tens digit
let h=hundredth digit
t+h=13
t=13-h
u=4
..
100h+10t+4-(100t+10h+4)=90
100h+10(13-h)+4-(100(13-h)+10h+4)=90
100h+130-10h+4-1300+100h-10h-4=90
200h-20h-1170=90
180h=1260
h=1260/180=7
t=13-h=6
original number: 764
..
Check: Interchange hundredth and tens digit
original-new number=764-674=90