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Sophie's favorite number is a two-digit number. If she reverses the digits, the result is 36 less than her favorite number. Also, one digit is 1 more than double the other digit. What is Sophie's favorite number?

 May 31, 2023
 #1
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Let Sophie's favorite number be 10a+b. We are told that if we reverse the digits, the result is 36 less than her favorite number. This means that 10b+a=10a+b−36 or 9a−9b=36 or a−b=4. We are also told that one digit is 1 more than double the other digit. This means that either a=2b+1 or b=2a+1. If a=2b+1, then a−b=4 implies that b=−3, which is not possible since b is a digit. Therefore, b=2a+1. Substituting this into a−b=4, we get a−2a−1=4 or a=5. Therefore, b=2(5)+1=11. Sophie's favorite number is 10(5)+11=61​.

 May 31, 2023
 #2
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(10a + b) - (10b + a) ==36.................(1)  

a==2b +  1..........................................(2), solve for a, b 

 

Use substitution to get:

a ==7

b==3

 

Hence, Sophie's favorite number is: 73

Check: 73  -  37 ==36, and:

              7 ==2*3 + 1

 May 31, 2023
 #3
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Let Sophie's favorite number be 10a+b, where a is the tens digit and b is the units digit. We know that a is 1 more than double b, so a=2b+1. We also know that if Sophie reverses the digits, the result is 36 less than her favorite number. This means that 10b+a=10a+b−36. We can solve this equation for a and b to get a=6 and b=2. Therefore, Sophie's favorite number is 10a+b=62​.

 May 31, 2023
 #4
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Let's start by writing down what we know about Sophie's favorite number:

It is a two-digit number.

If she reverses the digits, the result is 36 less than her favorite number.

One digit is 1 more than double the other digit.

We can use this information to set up a system of equations. Let x be the tens digit and y be the units digit. Then we have:

10x+y is Sophie's favorite number.

10y+x=10x+y−36.

x=2y+1.

We can solve this system of equations to get x=6 and y=2. Therefore, Sophie's favorite number is 10x+y=62​.

 Jun 1, 2023
 #5
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Let Sophie's favorite number be 10a + b, where a and b are the digits. We know that if she reverses the digits, the result is 36 less than her favorite number. This means that 10b + a = 10a + b - 36. We also know that one digit is 1 more than double the other digit. This means that a = 2b + 1.

We can solve for a and b by substituting the second equation into the first equation. This gives us 10(2b + 1) + b = 10(2b + 1) + b - 36. Simplifying, we get 20b + 10 + b = 20b + 10 - 36. This gives us b = 4. Substituting this into the equation a = 2b + 1, we get a = 9.

Therefore, Sophie's favorite number is 10a + b = 94.

 Jun 4, 2023

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