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?
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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
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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
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