QuestionFind three consecutive even integers that add up to 72.

Studdy Solution

STEP 1

Assumptions1. We are looking for three consecutive even integers. . The sum of these three integers is72.

STEP 2

Let's denote the three consecutive even integers as $n$ , $n+2$ , and $n+4$ . We choose $n+2$ and $n+4$ because even integers always differ by2.

STEP 3

Now, we can write the equation that represents the sum of these three integers.
$n + (n+2) + (n+) =72$

STEP 4

implify the equation by combining like terms.
$3n +6 =72$

STEP 5

Subtract from both sides of the equation to isolate the term with $n$ .
$3n =72 -$

STEP 6

Calculate the right side of the equation.
$3n =66$

STEP 7

Divide both sides of the equation by3 to solve for $n$ .
$n =66 /3$

STEP 8

Calculate the value of $n$ .
$n =22$

STEP 9

Now that we have the value of $n$ , we can find the other two integers by adding2 and4 to $n$ respectively.
$n+2 =22 +2$ $n+4 =22 +4$

STEP 10

Calculate the values of $n+2$ and $n+4$ .
$n+2 =24$ $n+4 =26$ The three consecutive even integers are22,24, and26.

Was this helpful?

QuestionFind three consecutive even integers that add up to 72.

Studdy Solution

STEP 1

Assumptions1. We are looking for three consecutive even integers. . The sum of these three integers is72.

STEP 2

Let's denote the three consecutive even integers as $n$ , $n+2$ , and $n+4$ . We choose $n+2$ and $n+4$ because even integers always differ by2.

STEP 3

Now, we can write the equation that represents the sum of these three integers.
$n + (n+2) + (n+) =72$

STEP 4

implify the equation by combining like terms.
$3n +6 =72$

STEP 5

Subtract from both sides of the equation to isolate the term with $n$ .
$3n =72 -$

STEP 6

Calculate the right side of the equation.
$3n =66$

STEP 7

Divide both sides of the equation by3 to solve for $n$ .
$n =66 /3$

STEP 8

Calculate the value of $n$ .
$n =22$

STEP 9

Now that we have the value of $n$ , we can find the other two integers by adding2 and4 to $n$ respectively.
$n+2 =22 +2$ $n+4 =22 +4$

STEP 10

Calculate the values of $n+2$ and $n+4$ .
$n+2 =24$ $n+4 =26$ The three consecutive even integers are22,24, and26.

Get Studdy

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.

QuestionFind three consecutive even integers that add up to 72.

Studdy Solution

STEP 1

Assumptions1. We are looking for three consecutive even integers. . The sum of these three integers is72.

STEP 2

Let's denote the three consecutive even integers as nnn, n+2n+2n+2, and n+4n+4n+4. We choose n+2n+2n+2 and n+4n+4n+4 because even integers always differ by2.

STEP 3

Now, we can write the equation that represents the sum of these three integers.n+(n+2)+(n+)=72n + (n+2) + (n+) =72n+(n+2)+(n+)=72

STEP 4

implify the equation by combining like terms.3n+6=723n +6 =723n+6=72

STEP 5

Subtract from both sides of the equation to isolate the term with nnn.3n=72−3n =72 -3n=72−

STEP 6

Calculate the right side of the equation.3n=663n =663n=66

STEP 7

Divide both sides of the equation by3 to solve for nnn.n=66/3n =66 /3n=66/3

STEP 8

Calculate the value of nnn.n=22n =22n=22

STEP 9

Now that we have the value of nnn, we can find the other two integers by adding2 and4 to nnn respectively.n+2=22+2n+2 =22 +2n+2=22+2n+4=22+4n+4 =22 +4n+4=22+4

STEP 10

Calculate the values of n+2n+2n+2 and n+4n+4n+4.n+2=24n+2 =24n+2=24n+4=26n+4 =26n+4=26The three consecutive even integers are22,24, and26.

Get Studdy

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.

Let's denote the three consecutive even integers as $n$ , $n+2$ , and $n+4$ . We choose $n+2$ and $n+4$ because even integers always differ by2.

Now, we can write the equation that represents the sum of these three integers.
$n + (n+2) + (n+) =72$

implify the equation by combining like terms.
$3n +6 =72$

Subtract from both sides of the equation to isolate the term with $n$ .
$3n =72 -$

Calculate the right side of the equation.
$3n =66$

Divide both sides of the equation by3 to solve for $n$ .
$n =66 /3$

Calculate the value of $n$ .
$n =22$

Now that we have the value of $n$ , we can find the other two integers by adding2 and4 to $n$ respectively.
$n+2 =22 +2$ $n+4 =22 +4$

Calculate the values of $n+2$ and $n+4$ .
$n+2 =24$ $n+4 =26$ The three consecutive even integers are22,24, and26.