QuestionFind two consecutive numbers whose sum is $2n + 1$ . What are the numbers?

Studdy Solution

STEP 1

Assumptions1. We have two consecutive numbers. The sum of these two numbers is $n +1$

STEP 2

Let's denote the smaller of the two consecutive numbers as $x$ . Then, the next number, being consecutive, is $x +1$ .

STEP 3

According to the problem, the sum of these two numbers is $2n +1$ . So, we can write the equation as $x + (x +1) =2n +1$

STEP 4

implify the left side of the equation by combining like terms.
$2x +1 =2n +1$

STEP 5

To find the value of $x$ , we can set the right side of the equation equal to the left side and solve for $x$ .
$2x =2n$

STEP 6

Divide both sides of the equation by2 to solve for $x$ .
$x = n$

STEP 7

Now that we have the value of $x$ , we can find the next consecutive number by adding1 to $x$ .
$x +1 = n +1$ So, the two consecutive numbers are $n$ and $n +1$ .

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QuestionFind two consecutive numbers whose sum is $2n + 1$ . What are the numbers?

Studdy Solution

STEP 1

Assumptions1. We have two consecutive numbers. The sum of these two numbers is $n +1$

STEP 2

Let's denote the smaller of the two consecutive numbers as $x$ . Then, the next number, being consecutive, is $x +1$ .

STEP 3

According to the problem, the sum of these two numbers is $2n +1$ . So, we can write the equation as $x + (x +1) =2n +1$

STEP 4

implify the left side of the equation by combining like terms.
$2x +1 =2n +1$

STEP 5

To find the value of $x$ , we can set the right side of the equation equal to the left side and solve for $x$ .
$2x =2n$

STEP 6

Divide both sides of the equation by2 to solve for $x$ .
$x = n$

STEP 7

Now that we have the value of $x$ , we can find the next consecutive number by adding1 to $x$ .
$x +1 = n +1$ So, the two consecutive numbers are $n$ and $n +1$ .

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QuestionFind two consecutive numbers whose sum is 2n+12n + 12n+1. What are the numbers?

Studdy Solution

STEP 1

Assumptions1. We have two consecutive numbers. The sum of these two numbers is n+1n +1n+1

STEP 2

Let's denote the smaller of the two consecutive numbers as xxx. Then, the next number, being consecutive, is x+1x +1x+1.

STEP 3

According to the problem, the sum of these two numbers is 2n+12n +12n+1. So, we can write the equation asx+(x+1)=2n+1x + (x +1) =2n +1x+(x+1)=2n+1

STEP 4

implify the left side of the equation by combining like terms.2x+1=2n+12x +1 =2n +12x+1=2n+1

STEP 5

To find the value of xxx, we can set the right side of the equation equal to the left side and solve for xxx.2x=2n2x =2n2x=2n

STEP 6

Divide both sides of the equation by2 to solve for xxx.x=nx = nx=n

STEP 7

Now that we have the value of xxx, we can find the next consecutive number by adding1 to xxx.x+1=n+1x +1 = n +1x+1=n+1So, the two consecutive numbers are nnn and n+1n +1n+1.

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QuestionFind two consecutive numbers whose sum is $2n + 1$ . What are the numbers?

Assumptions1. We have two consecutive numbers. The sum of these two numbers is $n +1$

Let's denote the smaller of the two consecutive numbers as $x$ . Then, the next number, being consecutive, is $x +1$ .

According to the problem, the sum of these two numbers is $2n +1$ . So, we can write the equation as $x + (x +1) =2n +1$

implify the left side of the equation by combining like terms.
$2x +1 =2n +1$

To find the value of $x$ , we can set the right side of the equation equal to the left side and solve for $x$ .
$2x =2n$

Divide both sides of the equation by2 to solve for $x$ .
$x = n$

Now that we have the value of $x$ , we can find the next consecutive number by adding1 to $x$ .
$x +1 = n +1$ So, the two consecutive numbers are $n$ and $n +1$ .