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 no?

Question 672493: 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 no?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = the 10's digit, y = the units
then
10x+y = "the number"
:
Write an equation for each statement:
:
"the tens digit of a number is 3 less than the units digit."
x = y - 3
:
"the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3."
= 4 (subtracting the remainder makes it come out even)
:
multiply both sides by (x+y), results:
10x + y - 3 = 4(x+y)
:
10x + y - 3 = 4x + 4y
:
10x - 4x + y - 4y = 3
:
6x - 3y = 3
:
simplify, divide by 3
2x - y = 1
:
replace x with (y-3); (from the 1st statement)
2(y-3) - y = 1
2y - 6 - y = 1
y = 1 + 6
y = 7 is the units digit
then
7 -3 = 4 is the 10's digit
:
what is the original no? 47
:
:
You can confirm this in the statement:
" the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3."
= 4, remainder of 3
:

RELATED QUESTIONS
The units digit of a two-digit number is 3 less than its tens digit. If the number is... (answered by josmiceli)

the units digit of a two-digit number is 3 less than its tens digit. if the number is... (answered by ankor@dixie-net.com)

The tens digits of a two digit number is 3 less than the units digit. If the number is... (answered by lwsshak3)

When a certain 3-digit number is divided by the number with the digits reversed, the... (answered by ankor@dixie-net.com)

The tens digit of a number is 3 less than the units digit. If the number is divided by... (answered by ankor@dixie-net.com)

the tens digit of a number is 3 less than the units digit. if the number is divided by... (answered by stanbon)

The tens digit of a number is 3 less than the units digit. If the number is divided by... (answered by ankor@dixie-net.com)

the tens digit of a number is 3 less than the units digit. if the numbers is divided by... (answered by josmiceli)

the units digit of a two-digit number is less than its tens digit. if the number is... (answered by edjones)