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
Algebra.Com
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(39617) (Show Source): You can put this solution on YOUR website!
t, for tens place
u, for units or ones place
Description:
(substitution using digit sum equation)
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Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
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
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