Question 551147: The sum of the digits of a certain two digit number is eight. If the original number is subtracted from the number formed by interchanging the digits, the result is -18. What is the original number? Please help!!!
Found 3 solutions by mathstutor458, josmiceli, lwsshak3:
Answer by mathstutor458(57)   (Show Source):
You can put this solution on YOUR website! let the two digit number is xy
The sum of the digits of a certain two digit number is 8
so, x+y=8
we have possibilities (1,7),(2,6)(3,5),(4,4) vice versa we cany take because,if the number formed by interchanging the digits is subtracted from the original number the result is -18.
first take, x=1,y=7
x+y=7
1+7=8
8=8
satisfies one condition,but we have to check other condition.i.e.,If the number formed by interchanging the digits is subtracted from the original number the result is -18.
Which means, xy-yx=-18
17-71=-18 not satisfied so x=1,y=7 are not.
take, x=2,y=6
x+y=8
2+6=8
8=8
satisfies one condition,but we have to check other condition also.i.e.,If the number formed by interchanging the digits is subtracted from the original number the result is -18.
xy-yx=-18
26-62=-18 not satisfies the condition.
take, x=3,y=5
x+y=8
3+5=8
8=8
satisfies one condition,but we have to check other condition also.i.e.,If the number formed by interchanging the digits is subtracted from the original number the result is -18.
xy-yx=-18
35-53=-18 satisfies the condition.
so , solutions are x=3,y=5
original number =35----->answer
Answer by josmiceli(19441)  (Show Source):
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! The sum of the digits of a certain two digit number is eight. If the original number is subtracted from the number formed by interchanging the digits, the result is -18. What is the original number?
**
let t=ten's digit
let u=unit's digit
t+u=8, t=8-u
original no.=10t+u
interchanged no.=10u+t
..
10u+t-(10t+u)=-18
10u+t-10t-u=-18
10u+8-u-10(8-u)-u=-18
10u+8-u-80+10u-u=-18
18u=54
u=3
t=8-u=5
original number=53
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