SOLUTION: The tens digit of a number is 3 less than the units digit. If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3. What is the original number?

Question 475433: The tens digit of a number is 3 less than the units digit. If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3. What is the original number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
x = the 10's digit
y = the units
10x + y = the number
:
"The tens digit of a number is 3 less than the units digit."
y - x = 3
y = (x+3)
:
If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3.
= 4
multiply both sides by (x+y)
10x + y - 3 = 4(x+y)
10x + y - 3 = 4x + 4y
10x - 4x = 4y - y + 3
6x = 3y + 3
Simplify divide by 3
2x = y + 1
replace y with (x+3)
2x = x + 3 + 1
2x - x = 4
x = 4 is the tens digit
then
y = 4 + 3
y = 7 is the units
:
47 is the original number
:
:
See if that works in the statement:
"If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3."
= 4 a remainder of 3

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