SOLUTION: the tens' digit of a two-digit number is one more than the units' digit. if the number is divided by the sum of the digits, the quotient is equal to 7. what is the number?
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Question 500933: the tens' digit of a two-digit number is one more than the units' digit. if the number is divided by the sum of the digits, the quotient is equal to 7. what is the number? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! the tens' digit of a two-digit number is one more than the units' digit.if the number is divided by the sum of the digits, the quotient is equal to 7.
what is the number?
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Let x & y be the two digits, then 10x+y is the number
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Write an equation for each statement:
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"the tens' digit is one more than the units' digit."
x = y + 1
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"if the number is divided by the sum of the digits, the quotient is equal to 7." = 7
Multiply both sides by(x+y), results
10x + y = 7(x+y)
10x + y = 7x + 7y
10x - 7x = 7y - y
3x = 6y
Replace x with (y+1), from the 1st statement
3(y+1) = 6y
3y + 3 = 6y
3 = 6y - 3y
3 = 3y
y = 1
then obviously x=2
:
21 is the number
;
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Check this using the 2nd statement
"the number is divided by the sum of the digits, the quotient is equal to 7." = 7
