+842 Sophie's favorite (positive) number is a two-digit number. If she reverses the digits, the result is 72 less than her favorite number. Also, one digit is 1 less than double the other digit. What is Sophie's favorite number?
+1926 Let's write an equation to solve this pronlem.
First off, let's let x be the tens digit and the other be y.
From the first of the problem, we have the equation
\(10x+y = 10y+x +72\)
From the second part of the problem, we have the equation
\(x=2y-1\)
Solving this system, we get that \(x=17,\:y=9\)
This equation cannot be satisfied.
From the first equation, we have that \(y=x-8\)
There are only two possibilities. One is where x is 9 and y is 1, so we have 91.
The other possibility is x is 8 and y is 0.
Neither of these satisfy the conditions given.
Thanks! :)
+1926 Let's write an equation to solve this pronlem.
First off, let's let x be the tens digit and the other be y.
From the first of the problem, we have the equation
\(10x+y = 10y+x +72\)
From the second part of the problem, we have the equation
\(x=2y-1\)
Solving this system, we get that \(x=17,\:y=9\)
This equation cannot be satisfied.
From the first equation, we have that \(y=x-8\)
There are only two possibilities. One is where x is 9 and y is 1, so we have 91.
The other possibility is x is 8 and y is 0.
Neither of these satisfy the conditions given.
Thanks! :)
