Question 471068
1.The sum of the digits of a 2 digits number is 8.if the digits of the number are reversed, the number formed is 36 more than the number. what is the number
:
Let a = the 10's digit
Let b = the units
:
"The sum of the digits of a 2 digits number is 8."
a + b = 8
b = (8-a)
:
"if the digits of the number are reversed,the number formed is 36 more than the number."
10b + a = 10a + b + 36
10b - b = 10a - a + 36
9b = 9a + 36
simplify, divide by 9
b = a + 4
Replace b with (8-a)
8 - a = a + 4
8 - 4 = a + a
4 = 2a
a = {{{4/2}}}
a = 2, 
then
b = 8 - 2
b = 6
:
then 26 is the original two digit number