SOLUTION: 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.

Algebra ->  Human-and-algebraic-language -> SOLUTION: 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.      Log On


   

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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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
%28%2810a%29%2B+b+-+6%29%2F%28a%2Bb%29 = 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