# 1. The sum of the digits of a two-digit number is 11. If we interchanged the digits then the new number formed is 45 less than the original. Find the original number and give it's working equation, given, solution, valuation, and final answer.

2
by tagasaclarice

2014-01-08T19:18:35+08:00
Let x be the 1st digit and y be the 2nd digit
10x+y be the original no. and 10y+x be the new no.

i)x+y=11
ii)10y+x=10x+y-45 it becomes -9x+9y=-45

i)9(x+y)=11(9)=   9x+9y=99
+-9x+9y=-45
18y=54
18   18
y=3
if y=3
i)x+y=11
x+3=11
x=11-3
x=8

so the final ans. will be 83
2014-01-09T16:44:24+08:00
t = 10's digit
u = 1's digit

t + u = 11
10u + t = 45 + (10t + u)

This second equation is the tricky part. It says that the VALUE of the reversed number (10 times the unit's digit added to the ten's digit itself) is equal to 45 more than the original number (10 times the ten's digit added to the unit's digit)

Combine like terms: 9u - 9t = 45
Solve by elimination:

9u - 9t = 45
-9u -9t = -99

-18t = -54

t = 3, u = 8

Original number is 38.

EDIT: xjroll, I teach math for a living, so I think I should remember this. :D

Which reminds me... I'm not getting paid for this! Time to go home! :)
Asker's rating & comment awww thxss thts what the answerr was at the end thnxss aloot i appriciatee itt ;))