SOLUTION: A two digit number is such that the sum of the digits is 12 if the digits are interchanged the value of the new number formed is15 more than twice the value of the original number

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Question 1207157: A two digit number is such that the sum of the digits is 12 if the digits are interchanged the value of the new number formed is15 more than twice the value of the original number find the original number
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39616) About Me  (Show Source):
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t, for tens place
u, for units or ones place
10t%2Bu

Description:
system%28t%2Bu=12%2C10u%2Bt=15%2B2%2810t%2Bu%29%29


10u%2Bt=15%2B2%2A10t%2B2%2Au
10u%2Bt=15%2B20t%2B2u
8u=15%2B19t
8%2812-t%29=15%2B19t (substitution using digit sum equation)
96-8t=15%2B19t
96-15=19t%2B8t
81=27t
t=3------------u=9

Answer by mananth(16946) About Me  (Show Source):
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A two digit number is such that the sum of the digits is 12 if the digits are interchanged the value of the new number formed is15 more than twice the value of the original number find the original number
Let ten's digit be x
and the units digit be y
the sum of the digits is 12
x+y=12..............................1
if the digits are interchanged the value of the new number formed is15 more than twice the value of the original number
Value of original number = 10x+Y
Reverse number will be 10y+x
10y+x = 15+2(10x+y)

10y+x = 15+20x+2y
rearrange
10y-2y +x-20x = 15
8y-19x = 15.......................2
solve 1 & 2
Multiply (1) by -8
-8x-8y= -96..................3
add (1) &(3)
-27x = -81
x = 3
now x+y =12
so y = 12-3 = 9
So the number is 39
check

93 = 15+2(39)
93 = 15+ 78=93
LHS = RHS