MHB Simultaneous equations number problem

AI Thread Summary
The problem involves a two-digit number where the tens digit is represented as $x$ and the units digit as $y$, with the equations $x + y = 15$ and $y - x = 3$. The initial setup incorrectly states the sum of the digits, leading to confusion in solving the simultaneous equations. By correctly interpreting the equations, the relationship between the digits can be established. The solution reveals that the digits can be solved to find the correct number, which is essential for confirming the calculations. The discussion emphasizes the importance of accurately setting up the equations based on the problem's conditions.
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A certain numbers tenth place digit is $x$ & unit place digit is $1$. That number can be written as $(10x+y)$ . The sum of those two digits is 15 . When those two digits are flipped a number is made, That number less the first number results in 27.

What Have I done so far

$10x+y=15$
$(10y+x)-(10x+y)=27=9y-9x=27=y-x=3$

$y-x=3$
$10x+y=15$

Now solving the two simultaneous equations by subtraction,

11x=12

Now by substituting the thing in 1 I get y=5

Now the digit is 501-105=27 which is incorrect

Where have I done wrong ?

Many Thanks :)
 
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I'm guessing you mean to say the tens digint is $x$ and the unit digit is $y$ such that the number is:

$$10x+y$$

We are told:

$$x+y=15$$ (this is where you went wrong...you just want to add the digits here)

and

$$(10y+x)-(10x+y)=27$$ which simplifies to:

$$y-x=3$$

Can you proceed?
 
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