SOLUTION: the units digit of a two-digit number is 3 less than its tens digit. if the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8. find the number.

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Question 150595: the units digit of a two-digit number is 3 less than its tens digit. if the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8. find the number.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the units digit of a two-digit number is 3 less than its tens digit. if the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8. find the number.
:
Let x = the 10's digit
then
(x-3) = the units digit
:
The number: 10x + (x-3) which can be written 11x-3
:
Write an equation for the statement:
"if the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8."
(subtract the remainder to make it come out even)
%28%2811x-3%29-8%29%2F%28%28x+%2B+%28x-3%29%29%29 = 6
:
%28%2811x-11%29%29%2F%28%282x-3%29%29%29 = 6
:
Multiply both sides by (2x-3)
11x - 11 = 6(2x-3)
:
11x - 11 = 12x - 18
:
-11 + 18 = 12x - 11x
:
x = 7 is the 10's digit
then
7 - 3 = 4 is the units digit
:
Our number is 74
:
Check the solution by dividing it by the sum which is 11
That gives you 6 with a remainder of 8