Question 300947
when the digits of a two-digit number are reversed,the new number is 9 more than the original number,
and the sum of the digits of the original number is 11.
What is the original number?
:
Let x = the 10's digit
Let y = the units digit
:
10x + y = the original number
and
10y + x = the reversed number
:
The equation for the statement:
"the digits of a two-digit number are reversed,the new number is 9 more than the original number,"
10y + x = 10x + y + 9
combine y's on the left and x's on the right
10y - y = 10x - x + 9
9y = 9x + 9
simplify, divide by 9
y = x + 1
:
"the sum of the digits of the original number is 11."
x + y = 11
From the 1st equation substitute (x+1) for y
x + (x+1) = 11
2x = 11 - 1
2x = 10
x= 10/2
x = 5
then
y = 5 + 1
y = 6
:
What is the original number? 56 is the original number
:
:
See if that satisfies the 1st statement:
"the digits of a two-digit number are reversed,the new number is 9 more than the original number,
65 = 56 + 9; confirms our solution