Question 724360
let a = the 10's digit
let b = the units
then
10a+b = "the number"
:
Write an equation for each statement
:
"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 is 7 and the remainder is 6."
subtract the remainder (6) from the number to get an even 7
{{{((10a+b-6))/((a+b))}}} = 7
multiply both sides by (a+b)
10a + b - 6 = 7(a+b)
10a + b - 6 = 7a + 7b
10a - 7a = 7b - b + 6
3a = 6b + 6
simplify, divide by 3
a = 2b + 2
Replace a with (b+5)
b + 5 = 2b + 2
5 - 2 = 2b - b
b = 3, 
then
a = 3 + 5
a = 8
:
83 is the number
:
:

Check this, divide 83 by 11, 7 a remainder of 6