Math / Algebra

Question3. The difference of the digits of a two-digit number is 5 . When the digits are reversed, the number decreases by 45 . Find the original number.
161, ว2, 83,94

Studdy Solution

STEP 1

1. The original number is a two-digit number.
2. The difference between the digits of the number is 5.
3. Reversing the digits decreases the number by 45.
4. We need to find the original number.

STEP 2

1. Define variables for the digits of the number.
2. Set up equations based on the problem statements.
3. Solve the system of equations to find the digits.
4. Construct the original number from the digits.

STEP 3

Define variables for the digits of the number.
Let $x$ be the tens digit and $y$ be the units digit of the original number.

STEP 4

Set up equations based on the problem statements.
From the problem, we have two key pieces of information: - The difference of the digits is 5: $ x - y = 5 \]
- Reversing the digits decreases the number by 45: $ 10x + y - (10y + x) = 45 \]

STEP 5

Simplify and solve the system of equations.
Simplify the second equation: $10x + y - 10y - x = 45 \\ 9x - 9y = 45 \\ x - y = 5$
We notice that the second equation simplifies to the first equation, confirming consistency.

STEP 6

Solve the equation $x - y = 5$ .
Since the equation $x - y = 5$ is already simplified, we can solve for one variable in terms of the other. Let's express $x$ in terms of $y$ : $x = y + 5$

STEP 7

Construct the original number from the digits.
Since the tens digit $x = y + 5$ , and both $x$ and $y$ must be digits (0 through 9), find suitable values: - If $y = 2$ , then $x = 2 + 5 = 7$ .
Therefore, the original number is: \[ 10x + y = 10(7) + 2 = 72$
The original number is $\boxed{72}$ .

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Question3. The difference of the digits of a two-digit number is 5 . When the digits are reversed, the number decreases by 45 . Find the original number.
161, ว2, 83,94

Studdy Solution

STEP 1

1. The original number is a two-digit number.
2. The difference between the digits of the number is 5.
3. Reversing the digits decreases the number by 45.
4. We need to find the original number.

STEP 2

1. Define variables for the digits of the number.
2. Set up equations based on the problem statements.
3. Solve the system of equations to find the digits.
4. Construct the original number from the digits.

STEP 3

Define variables for the digits of the number.
Let $x$ be the tens digit and $y$ be the units digit of the original number.

STEP 4

Set up equations based on the problem statements.
From the problem, we have two key pieces of information: - The difference of the digits is 5: $ x - y = 5 \]
- Reversing the digits decreases the number by 45: $ 10x + y - (10y + x) = 45 \]

STEP 5

Simplify and solve the system of equations.
Simplify the second equation: $10x + y - 10y - x = 45 \\ 9x - 9y = 45 \\ x - y = 5$
We notice that the second equation simplifies to the first equation, confirming consistency.

STEP 6

Solve the equation $x - y = 5$ .
Since the equation $x - y = 5$ is already simplified, we can solve for one variable in terms of the other. Let's express $x$ in terms of $y$ : $x = y + 5$

STEP 7

Construct the original number from the digits.
Since the tens digit $x = y + 5$ , and both $x$ and $y$ must be digits (0 through 9), find suitable values: - If $y = 2$ , then $x = 2 + 5 = 7$ .
Therefore, the original number is: \[ 10x + y = 10(7) + 2 = 72$
The original number is $\boxed{72}$ .

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Question3. The difference of the digits of a two-digit number is 5 . When the digits are reversed, the number decreases by 45 . Find the original number.161, ว2, 83,94

Studdy Solution

STEP 1

1. The original number is a two-digit number.2. The difference between the digits of the number is 5.3. Reversing the digits decreases the number by 45.4. We need to find the original number.

STEP 2

1. Define variables for the digits of the number.2. Set up equations based on the problem statements.3. Solve the system of equations to find the digits.4. Construct the original number from the digits.

STEP 3

Define variables for the digits of the number.Let x x x be the tens digit and y y y be the units digit of the original number.

STEP 4

Set up equations based on the problem statements.From the problem, we have two key pieces of information: - The difference of the digits is 5: $ x - y = 5 \]- Reversing the digits decreases the number by 45: $ 10x + y - (10y + x) = 45 \]

STEP 5

Simplify and solve the system of equations.Simplify the second equation: 10x+y−10y−x=459x−9y=45x−y=510x + y - 10y - x = 45 \\ 9x - 9y = 45 \\ x - y = 510x+y−10y−x=459x−9y=45x−y=5We notice that the second equation simplifies to the first equation, confirming consistency.

STEP 6

Solve the equation x−y=5 x - y = 5 x−y=5.Since the equation x−y=5 x - y = 5 x−y=5 is already simplified, we can solve for one variable in terms of the other. Let's express x x x in terms of y y y: x=y+5x = y + 5x=y+5

STEP 7

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Question3. The difference of the digits of a two-digit number is 5 . When the digits are reversed, the number decreases by 45 . Find the original number.
161, ว2, 83,94

1. The original number is a two-digit number.
2. The difference between the digits of the number is 5.
3. Reversing the digits decreases the number by 45.
4. We need to find the original number.

1. Define variables for the digits of the number.
2. Set up equations based on the problem statements.
3. Solve the system of equations to find the digits.
4. Construct the original number from the digits.

Define variables for the digits of the number.
Let $x$ be the tens digit and $y$ be the units digit of the original number.

Set up equations based on the problem statements.
From the problem, we have two key pieces of information: - The difference of the digits is 5: $ x - y = 5 \]
- Reversing the digits decreases the number by 45: $ 10x + y - (10y + x) = 45 \]

Simplify and solve the system of equations.
Simplify the second equation: $10x + y - 10y - x = 45 \\ 9x - 9y = 45 \\ x - y = 5$
We notice that the second equation simplifies to the first equation, confirming consistency.

Solve the equation $x - y = 5$ .
Since the equation $x - y = 5$ is already simplified, we can solve for one variable in terms of the other. Let's express $x$ in terms of $y$ : $x = y + 5$