a number consists of two digits whose sum is 9. if 45 is subtracted from the number its digits are interchanged. find the number.
X+y=9
10x+y-45=10y+x
x+y=9.......(1)
10x-x+y-10y=45
9x-9y=45
9(x-y)=45
x-y=45
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x+y=9
x-y=5
2x=14
x=7
your turn finish it
7+y=9
y=9-7
y=2
the number is 72
Thanks you I give you like
X+y=9
10x+y-45=10y+x
solve it an algebra now
I am not understanding please explain me
thnx for the help
To find the number, let's start by breaking down the information given:
1. A number consists of two digits.
2. The sum of these two digits is 9.
3. When 45 is subtracted from the number, the digits are interchanged.
Let's represent the digits using variables. Let the first digit be x, and the second digit be y.
From the information given, we can create two equations:
Equation 1: x + y = 9
(Since the sum of the digits is 9.)
Equation 2: 10x + y - 45 = 10y + x
(Since 45 is subtracted from the number and the digits are interchanged.)
To solve the equations, we can use substitution or elimination:
Using substitution:
From Equation 1, we can express x in terms of y: x = 9 - y
Substituting this value of x into Equation 2:
10*(9 - y) + y - 45 = 10y + (9 - y)
Expanding and simplifying the equation:
90 - 10y + y - 45 = 10y + 9 - y
45 - 9 = 10y + y - y - 10y
36 = 10y - 9y
36 = y
Therefore, y = 36.
Substituting this value of y back into Equation 1:
x + 36 = 9
x = 9 - 36
x = -27
However, since the question states that we are dealing with digits, and no negative digit exists, this solution is not valid.
Therefore, there is no valid solution for this problem based on the given information.