QuestionFind three consecutive odd integers where the sum of the first, twice the second, and three times the third equals 22.

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd numbers. . The sum of the first, two times the second, and three times the third is22.

STEP 2

Let's denote the three consecutive odd integers as $n$ , $n+2$ , and $n+4$ . This is because odd integers are always2 units apart.

STEP 3

According to the problem, the sum of the first, two times the second, and three times the third is22. We can write this as an equation $n +2(n+2) +3(n+) =22$

STEP 4

Now, we simplify the equation. First, distribute the2 and the3 inside the parentheses.
$n +2n +4 +3n +12 =22$

STEP 5

Combine like terms on the left side of the equation.
$n +16 =22$

STEP 6

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

STEP 7

implify 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

implify the right side of the equation to find the value of $n$ .
$n =$

STEP 10

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

STEP 11

Calculate the values of $n+$ and $n+4$ .
$n+ =3$ $n+4 =5$ The smallest of the three consecutive odd integers is. The second largest of the three consecutive odd integers is3. The largest of the three consecutive odd integers is5.

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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.

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd numbers. . The sum of the first, two times the second, and three times the third is22.

STEP 2

Let's denote the three consecutive odd integers as $n$ , $n+2$ , and $n+4$ . This is because odd integers are always2 units apart.

STEP 3

According to the problem, the sum of the first, two times the second, and three times the third is22. We can write this as an equation $n +2(n+2) +3(n+) =22$

STEP 4

Now, we simplify the equation. First, distribute the2 and the3 inside the parentheses.
$n +2n +4 +3n +12 =22$

STEP 5

Combine like terms on the left side of the equation.
$n +16 =22$

STEP 6

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

STEP 7

implify 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

implify the right side of the equation to find the value of $n$ .
$n =$

STEP 10

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

STEP 11

Calculate the values of $n+$ and $n+4$ .
$n+ =3$ $n+4 =5$ The smallest of the three consecutive odd integers is. The second largest of the three consecutive odd integers is3. The largest of the three consecutive odd integers is5.

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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.

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd numbers. . The sum of the first, two times the second, and three times the third is22.

STEP 2

Let's denote the three consecutive odd integers as nnn, n+2n+2n+2, and n+4n+4n+4. This is because odd integers are always2 units apart.

STEP 3

According to the problem, the sum of the first, two times the second, and three times the third is22. 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

Now, we simplify the equation. First, distribute the2 and the3 inside the parentheses.n+2n+4+3n+12=22n +2n +4 +3n +12 =22n+2n+4+3n+12=22

STEP 5

Combine like terms on the left side of the equation.n+16=22n +16 =22n+16=22

STEP 6

Subtract16 from both sides of the equation to isolate the term with nnn.6n=22−166n =22 -166n=22−16

STEP 7

implify the right side of the equation.6n=66n =66n=6

STEP 8

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

STEP 9

implify the right side of the equation to find the value of nnn.n=n =n=

STEP 10

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

STEP 11

Calculate the values of n+n+n+ and n+4n+4n+4.n+=3n+ =3n+=3n+4=5n+4 =5n+4=5The smallest of the three consecutive odd integers is. The second largest of the three consecutive odd integers is3. The largest of the three consecutive odd integers is5.

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Let's denote the three consecutive odd integers as $n$ , $n+2$ , and $n+4$ . This is because odd integers are always2 units apart.

According to the problem, the sum of the first, two times the second, and three times the third is22. We can write this as an equation $n +2(n+2) +3(n+) =22$

Now, we simplify the equation. First, distribute the2 and the3 inside the parentheses.
$n +2n +4 +3n +12 =22$

Combine like terms on the left side of the equation.
$n +16 =22$

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

implify the right side of the equation.
$6n =6$

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

implify the right side of the equation to find the value of $n$ .
$n =$

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

Calculate the values of $n+$ and $n+4$ .
$n+ =3$ $n+4 =5$ The smallest of the three consecutive odd integers is. The second largest of the three consecutive odd integers is3. The largest of the three consecutive odd integers is5.