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?
:
Let x & y be the two digits, then 10x+y is the number
:
Write an equation for each statement:
:
"the tens' digit is one more than the units' digit."
x = y + 1
:
"if the number is divided by the sum of the digits, the quotient is equal to 7."
{{{(10x+y)/(x+y)}}} = 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
;
:
Check this using the 2nd statement
"the number is divided by the sum of the digits, the quotient is equal to 7."
{{{21/3}}} = 7