The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?
53
Sum = 8 = 7+1 = 6+2 = 5+3 = 4+4
Select 5, and 3:
Original #: 53.
Reversed: 35.
Difference = 53-35 = 18.
Here is how you do this with algebra.
Let x = 10s digit
and y = units digit.
So the number is 10x + y
and you know that if you reverse the number it is 10y + x.
The problem tells you that
10x + y = 10y+x+18 which simplifies to
9x-9y=18
The second equation is x + y = 8. Solve those two equations simultaneously this way.
9x-9y = 18
x+y=8
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Multiply equation 2 by 9 and you have these two equations.
9x - 9y = 18
9x + 9y = 72
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add
18x = 90
x = 90/18 = 5 which is the 10s digit.
Since x + y = 8, then
5 + y = 8 and y = 8-5=3 which is the units digit so the number is 53
To solve this problem, we can let the tens digit be represented by x and the units digit be represented by y. The original number can then be expressed as 10x + y, and the reversed number can be expressed as 10y + x.
According to the problem, the sum of the digits is 8, so we have:
x + y = 8 -- (Equation 1)
And the reversed number is 18 less than the original number, so:
10y + x = 10x + y - 18 -- (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve using the method of substitution:
From Equation 1, we find that x = 8 - y.
Substituting this value of x in Equation 2, we have:
10y + (8 - y) = 10(8 - y) + y - 18.
Simplifying the equation further:
10y + 8 - y = 80 - 10y + y - 18,
9y + 8 = 80 - 9y - 18,
9y + 9y = 80 - 18 - 8,
18y = 54.
Dividing both sides of the equation by 18:
y = 54 / 18 = 3.
Now that we know the value of y, we can substitute it back into Equation 1 to find x:
x + 3 = 8,
x = 8 - 3 = 5.
Therefore, the original number is 10x + y = 10(5) + 3 = 53.