QuestionFind a two-digit number whose digits reversed decreases its value by 27, and the sum of its digits is 7.

Studdy Solution

STEP 1

Assumptions1. The number is a two-digit number. . When the digits of the number are reversed, its value decreases by27.
3. The sum of the digits of the number is7.

STEP 2

Let's denote the tens digit of the number as 'a' and the units digit as 'b'. So, the number can be represented as10a + b.

STEP 3

The reversed number would be10b + a.

STEP 4

According to the problem, the original number is27 more than the reversed number. We can write this as an equation $10a + b =10b + a +27$

STEP 5

implify the equation by moving all terms involving 'a' and 'b' to one side and the constant to the other side.
$9a -9b =27$

STEP 6

Divide the entire equation by9 to simplify it further.
$a - b =3$

STEP 7

We also know from the problem that the sum of the digits is7. We can write this as another equation $a + b =7$

STEP 8

Now we have a system of two equations\begin{align} a - b &=3 \\ a + b &=7\end{align}

STEP 9

We can solve this system of equations by adding the two equations together to eliminate 'b'.
$2a =$

STEP 10

Divide by2 to solve for 'a'.
$a =5$

STEP 11

Substitute 'a =5' into the second equation to solve for 'b'.
$5 + b =7$

STEP 12

Subtract5 from both sides to solve for 'b'.
$b =2$

STEP 13

So, the original number is52.
The number is52.

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QuestionFind a two-digit number whose digits reversed decreases its value by 27, and the sum of its digits is 7.

Studdy Solution

STEP 1

Assumptions1. The number is a two-digit number. . When the digits of the number are reversed, its value decreases by27.
3. The sum of the digits of the number is7.

STEP 2

Let's denote the tens digit of the number as 'a' and the units digit as 'b'. So, the number can be represented as10a + b.

STEP 3

The reversed number would be10b + a.

STEP 4

According to the problem, the original number is27 more than the reversed number. We can write this as an equation $10a + b =10b + a +27$

STEP 5

implify the equation by moving all terms involving 'a' and 'b' to one side and the constant to the other side.
$9a -9b =27$

STEP 6

Divide the entire equation by9 to simplify it further.
$a - b =3$

STEP 7

We also know from the problem that the sum of the digits is7. We can write this as another equation $a + b =7$

STEP 8

Now we have a system of two equations\begin{align} a - b &=3 \\ a + b &=7\end{align}

STEP 9

We can solve this system of equations by adding the two equations together to eliminate 'b'.
$2a =$

STEP 10

Divide by2 to solve for 'a'.
$a =5$

STEP 11

Substitute 'a =5' into the second equation to solve for 'b'.
$5 + b =7$

STEP 12

Subtract5 from both sides to solve for 'b'.
$b =2$

STEP 13

So, the original number is52.
The number is52.

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QuestionFind a two-digit number whose digits reversed decreases its value by 27, and the sum of its digits is 7.

Studdy Solution

STEP 1

Assumptions1. The number is a two-digit number. . When the digits of the number are reversed, its value decreases by27.3. The sum of the digits of the number is7.

STEP 2

Let's denote the tens digit of the number as 'a' and the units digit as 'b'. So, the number can be represented as10a + b.

STEP 3

The reversed number would be10b + a.

STEP 4

According to the problem, the original number is27 more than the reversed number. We can write this as an equation10a+b=10b+a+2710a + b =10b + a +2710a+b=10b+a+27

STEP 5

implify the equation by moving all terms involving 'a' and 'b' to one side and the constant to the other side.9a−9b=279a -9b =279a−9b=27

STEP 6

Divide the entire equation by9 to simplify it further.a−b=3a - b =3a−b=3

STEP 7

We also know from the problem that the sum of the digits is7. We can write this as another equationa+b=7a + b =7a+b=7

STEP 8

Now we have a system of two equations\begin{align*} a - b &=3 \\ a + b &=7\end{align*}

STEP 9

We can solve this system of equations by adding the two equations together to eliminate 'b'.2a=2a =2a=

STEP 10

Divide by2 to solve for 'a'.a=5a =5a=5

STEP 11

Substitute 'a =5' into the second equation to solve for 'b'.5+b=75 + b =75+b=7

STEP 12

Subtract5 from both sides to solve for 'b'.b=2b =2b=2

STEP 13

So, the original number is52.The number is52.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. The number is a two-digit number. . When the digits of the number are reversed, its value decreases by27.
3. The sum of the digits of the number is7.

According to the problem, the original number is27 more than the reversed number. We can write this as an equation $10a + b =10b + a +27$

implify the equation by moving all terms involving 'a' and 'b' to one side and the constant to the other side.
$9a -9b =27$

Divide the entire equation by9 to simplify it further.
$a - b =3$

We also know from the problem that the sum of the digits is7. We can write this as another equation $a + b =7$

Now we have a system of two equations\begin{align} a - b &=3 \\ a + b &=7\end{align}

We can solve this system of equations by adding the two equations together to eliminate 'b'.
$2a =$

Divide by2 to solve for 'a'.
$a =5$

Substitute 'a =5' into the second equation to solve for 'b'.
$5 + b =7$

Subtract5 from both sides to solve for 'b'.
$b =2$

So, the original number is52.
The number is52.