QuestionFind the greatest of three consecutive even numbers that add up to 60. Options: (a) 20 (b) 19 (c) 22 (d) 24 (e) None.

Studdy Solution

STEP 1

Assumptions1. We have three consecutive even numbers. . The sum of these three numbers is60.
3. We need to find the greatest of these three numbers.

STEP 2

Let's denote the three consecutive even numbers as $n$ , $n+2$ , and $n+4$ . This is because even numbers always differ by2.

STEP 3

Given that the sum of the three numbers is60, we can write this as an equation $n + (n+2) + (n+) =60$

STEP 4

implify the equation by combining like terms $3n +6 =60$

STEP 5

Subtract from both sides of the equation to isolate the term with $n$ $3n =60 -$

STEP 6

implify the right side of the equation $3n =54$

STEP 7

Divide both sides of the equation by3 to solve for $n$ $n =54 /3$

STEP 8

Calculate the value of $n$ $n =18$

STEP 9

Now that we have the value of $n$ , we can find the greatest number by calculating the value of $n+4$ $Greatest\, number = n +4$

STEP 10

Substitute the value of $n$ into the equation to find the greatest number $Greatest\, number =18 +4$

STEP 11

Calculate the greatest number $Greatest\, number =22$ So, the greatest number is22.

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QuestionFind the greatest of three consecutive even numbers that add up to 60. Options: (a) 20 (b) 19 (c) 22 (d) 24 (e) None.

Studdy Solution

STEP 1

Assumptions1. We have three consecutive even numbers. . The sum of these three numbers is60.
3. We need to find the greatest of these three numbers.

STEP 2

Let's denote the three consecutive even numbers as $n$ , $n+2$ , and $n+4$ . This is because even numbers always differ by2.

STEP 3

Given that the sum of the three numbers is60, we can write this as an equation $n + (n+2) + (n+) =60$

STEP 4

implify the equation by combining like terms $3n +6 =60$

STEP 5

Subtract from both sides of the equation to isolate the term with $n$ $3n =60 -$

STEP 6

implify the right side of the equation $3n =54$

STEP 7

Divide both sides of the equation by3 to solve for $n$ $n =54 /3$

STEP 8

Calculate the value of $n$ $n =18$

STEP 9

Now that we have the value of $n$ , we can find the greatest number by calculating the value of $n+4$ $Greatest\, number = n +4$

STEP 10

Substitute the value of $n$ into the equation to find the greatest number $Greatest\, number =18 +4$

STEP 11

Calculate the greatest number $Greatest\, number =22$ So, the greatest number is22.

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QuestionFind the greatest of three consecutive even numbers that add up to 60. Options: (a) 20 (b) 19 (c) 22 (d) 24 (e) None.

Studdy Solution

STEP 1

Assumptions1. We have three consecutive even numbers. . The sum of these three numbers is60.3. We need to find the greatest of these three numbers.

STEP 2

Let's denote the three consecutive even numbers as nnn, n+2n+2n+2, and n+4n+4n+4. This is because even numbers always differ by2.

STEP 3

Given that the sum of the three numbers is60, we can write this as an equationn+(n+2)+(n+)=60n + (n+2) + (n+) =60n+(n+2)+(n+)=60

STEP 4

implify the equation by combining like terms3n+6=603n +6 =603n+6=60

STEP 5

Subtract from both sides of the equation to isolate the term with nnn3n=60−3n =60 -3n=60−

STEP 6

implify the right side of the equation3n=543n =543n=54

STEP 7

Divide both sides of the equation by3 to solve for nnnn=54/3n =54 /3n=54/3

STEP 8

Calculate the value of nnnn=18n =18n=18

STEP 9

Now that we have the value of nnn, we can find the greatest number by calculating the value of n+4n+4n+4Greatest number=n+4Greatest\, number = n +4Greatestnumber=n+4

STEP 10

Substitute the value of nnn into the equation to find the greatest numberGreatest number=18+4Greatest\, number =18 +4Greatestnumber=18+4

STEP 11

Calculate the greatest numberGreatest number=22Greatest\, number =22Greatestnumber=22So, the greatest number is22.

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Assumptions1. We have three consecutive even numbers. . The sum of these three numbers is60.
3. We need to find the greatest of these three numbers.

Let's denote the three consecutive even numbers as $n$ , $n+2$ , and $n+4$ . This is because even numbers always differ by2.

Given that the sum of the three numbers is60, we can write this as an equation $n + (n+2) + (n+) =60$

implify the equation by combining like terms $3n +6 =60$

Subtract from both sides of the equation to isolate the term with $n$ $3n =60 -$

implify the right side of the equation $3n =54$

Divide both sides of the equation by3 to solve for $n$ $n =54 /3$

Calculate the value of $n$ $n =18$

Now that we have the value of $n$ , we can find the greatest number by calculating the value of $n+4$ $Greatest\, number = n +4$

Substitute the value of $n$ into the equation to find the greatest number $Greatest\, number =18 +4$

Calculate the greatest number $Greatest\, number =22$ So, the greatest number is22.