QuestionFind three consecutive odd integers where the sum of the first, twice the second, and three times the third equals 22. The smallest is 1. What is the second largest?

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd integers. . The sum of the first integer, two times the second integer, and three times the third integer is22.
3. The smallest of the three consecutive odd integers is1.

STEP 2

Let's denote the three consecutive odd integers as $n$ , $n+2$ , and $n+4$ .

STEP 3

We know that the sum of the first integer, two times the second integer, and three times the third integer is22. So, we can write this as an equation $n +2(n+2) +3(n+) =22$

STEP 4

implify the equation by distributing the2 and the3 $n +2n +4 +3n +12 =22$

STEP 5

Combine like terms $n +16 =22$

STEP 6

Subtract16 from both sides of the equation to isolate the variable $6n =22 -16$

STEP 7

Calculate the right side of the equation $6n =6$

STEP 8

Divide both sides of the equation by6 to solve for $n$ $n =6 /6$

STEP 9

Calculate the value of $n$ $n =$

STEP 10

Now that we have the value of $n$ , we can find the second largest of the three consecutive odd integers by calculating $n+2$ $n+2 =+2$

STEP 11

Calculate the value of $n+$ $n+ =3$ The second largest of the three consecutive odd integers is3.

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QuestionFind three consecutive odd integers where the sum of the first, twice the second, and three times the third equals 22. The smallest is 1. What is the second largest?

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd integers. . The sum of the first integer, two times the second integer, and three times the third integer is22.
3. The smallest of the three consecutive odd integers is1.

STEP 2

Let's denote the three consecutive odd integers as $n$ , $n+2$ , and $n+4$ .

STEP 3

We know that the sum of the first integer, two times the second integer, and three times the third integer is22. So, we can write this as an equation $n +2(n+2) +3(n+) =22$

STEP 4

implify the equation by distributing the2 and the3 $n +2n +4 +3n +12 =22$

STEP 5

Combine like terms $n +16 =22$

STEP 6

Subtract16 from both sides of the equation to isolate the variable $6n =22 -16$

STEP 7

Calculate the right side of the equation $6n =6$

STEP 8

Divide both sides of the equation by6 to solve for $n$ $n =6 /6$

STEP 9

Calculate the value of $n$ $n =$

STEP 10

Now that we have the value of $n$ , we can find the second largest of the three consecutive odd integers by calculating $n+2$ $n+2 =+2$

STEP 11

Calculate the value of $n+$ $n+ =3$ The second largest of the three consecutive odd integers is3.

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QuestionFind three consecutive odd integers where the sum of the first, twice the second, and three times the third equals 22. The smallest is 1. What is the second largest?

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd integers. . The sum of the first integer, two times the second integer, and three times the third integer is22.3. The smallest of the three consecutive odd integers is1.

STEP 2

Let's denote the three consecutive odd integers as nnn, n+2n+2n+2, and n+4n+4n+4.

STEP 3

We know that the sum of the first integer, two times the second integer, and three times the third integer is22. So, we can write this as an equationn+2(n+2)+3(n+)=22n +2(n+2) +3(n+) =22n+2(n+2)+3(n+)=22

STEP 4

implify the equation by distributing the2 and the3n+2n+4+3n+12=22n +2n +4 +3n +12 =22n+2n+4+3n+12=22

STEP 5

Combine like termsn+16=22n +16 =22n+16=22

STEP 6

Subtract16 from both sides of the equation to isolate the variable6n=22−166n =22 -166n=22−16

STEP 7

Calculate the right side of the equation6n=66n =66n=6

STEP 8

Divide both sides of the equation by6 to solve for nnnn=6/6n =6 /6n=6/6

STEP 9

Calculate the value of nnnn=n =n=

STEP 10

Now that we have the value of nnn, we can find the second largest of the three consecutive odd integers by calculating n+2n+2n+2n+2=+2n+2 =+2n+2=+2

STEP 11

Calculate the value of n+n+n+n+=3n+ =3n+=3The second largest of the three consecutive odd integers is3.

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Assumptions1. The three integers are consecutive odd integers. . The sum of the first integer, two times the second integer, and three times the third integer is22.
3. The smallest of the three consecutive odd integers is1.

Let's denote the three consecutive odd integers as $n$ , $n+2$ , and $n+4$ .

We know that the sum of the first integer, two times the second integer, and three times the third integer is22. So, we can write this as an equation $n +2(n+2) +3(n+) =22$

implify the equation by distributing the2 and the3 $n +2n +4 +3n +12 =22$

Combine like terms $n +16 =22$

Subtract16 from both sides of the equation to isolate the variable $6n =22 -16$

Calculate the right side of the equation $6n =6$

Divide both sides of the equation by6 to solve for $n$ $n =6 /6$

Calculate the value of $n$ $n =$

Now that we have the value of $n$ , we can find the second largest of the three consecutive odd integers by calculating $n+2$ $n+2 =+2$

Calculate the value of $n+$ $n+ =3$ The second largest of the three consecutive odd integers is3.