SOLUTION: a two digit number is 5 times the sum of its digit. when 9 is added to the number the result is the original number with its reversed. find the original number

Question 148904: a two digit number is 5 times the sum of its digit. when 9 is added to the number the result is the original number with its reversed. find the original number
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
Let a and b the digits we can write the number as "ab" but the number is 10*a+b
(for example if a=3 and b=2 the number would be 32 and 32 =10*3+2)

a two digit number is 5 times the sum of its digit then 10*a+b=5(a+b)
when 9 is added to the number the result is the original number with its reversed 10*a+b+9=10*b+a
then we have the following equations:
10*a+b=5(a+b)
10*a+b+9=10*b+a
then
10a+b=5a+5b
10a+b+9=10b+a
then
5a-4b=0
9a-9b=-9
then
5a-4b=0
a-b=-1
then using 2nd eq a=b-1
using 1st eq 5(b-1)-4b=0
then 5b-5-4b=0
then b=5 and a=5-1=4
so the original number is 45

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