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# Algebra

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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?

Jul 18, 2024

#1
+1786
+1

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! :)

Jul 18, 2024
edited by NotThatSmart  Jul 18, 2024

#1
+1786
+1

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! :)

NotThatSmart Jul 18, 2024
edited by NotThatSmart  Jul 18, 2024