SOLUTION: A certain number with two digits is divided by the sum if the digits. The quotient is 6 and the remainder is 5. The difference between the number and the given number when reverse

Algebra ->  Equations -> SOLUTION: A certain number with two digits is divided by the sum if the digits. The quotient is 6 and the remainder is 5. The difference between the number and the given number when reverse       Log On


   

Question 968399: A certain number with two digits is divided by the sum if the digits. The quotient is 6 and the remainder is 5. The difference between the number and the given number when reverse is 18. Find the number?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a = 10's digit
b = units
then
10a + b = the number
:
A certain number with two digits is divided by the sum if the digits.
The quotient is 6 and the remainder is 5.
%28%2810a%2Bb%29-5%29%2F%28a%2Bb%29 = 6
10a + b -5 = 6(a+b)
10a + b - 5 = 6a + 6b
10a - 6a + b - 6b = 5
4a - 5b = 5
:
The difference between the number and the given number when reverse is 18.
(10a+b) - (10b+a) = 18
10a + b - 10b - a = 18
9a - 9b = 18
Simplify divide by 9
a - b = 2
a = b + 2
:
In the first equation replace a with (b+2)
4(b+2) - 5b = 5
4b + 8 - 5b = 5
4b - 5b = 5 - 8
-b = -3
b = 3
find a
a = 3 + 2
a = 5
:
Find the number? 53
:
:
Confirm this solution in the 1st statements
"A certain number with two digits is divided by the sum if the digits. The quotient is 6 and the remainder is 5."
%2853-5%29%2F%285%2B3%29 = 6
48/8 = 6
:
you can confirm this in the 2nd statement 53 - 35