Question 1109194
The tens digit of a two-digit number is 5 more than the units digit.
 If "the number" is divided by the sum of its digits, the partial quotient (answer) is 7 and the remainder is 6.
 Find the number.
let a = the 10's digit
let b = the units
then
10a+b = "the number"
:
" The tens digit of a two-digit number is 5 more than the units digit."
a = b + 5
:
If "the number" is divided by the sum of its digits, the partial quotient (answer) is 7 and the remainder is 6.
  Subtracting the remainder make the quotient an integer
{{{((10a)+ b - 6)/(a+b)}}} = 7
multiply both sides by (a+b)
10a + b - 6 = 7(a+b)
10a + b -6 = 7a + 7b
combine like terms on the left
10a - 7a + b - 7b = 6
3a - 6b = 6
simplify, divide by 3
a - 2b = 2
replace a with (b+5), from the first equation/statement
(b+5) - 2b = 2
b - 2b = 2 - 5
-b = -3
b = 3
then, obviously;
a = 8
 Find the number. 83 is the number 
:
;
Check
(83-6)/11 = 7