QuestionFind three consecutive odd integers where the sum of the smallest and middle integer equals 51 more than the largest.

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd integers. . The sum of the least and middle integer is51 more than the greatest integer.

STEP 2

Let's denote the three consecutive odd integers as $x$ , $x+2$ , and $x+4$ . The reason we're adding2 each time is because odd numbers are always2 units apart.

STEP 3

According to the problem, the sum of the least integer and the middle integer is51 more than the greatest integer. We can write this as an equation $x + (x+2) = (x+) +51$

STEP 4

implify the equation by combining like terms on each side.
$2x +2 = x +55$

STEP 5

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$x +2 =55$

STEP 6

Subtract2 from both sides of the equation to solve for $x$ .
$x =55 -2$

STEP 7

Calculate the value of $x$ .
$x =53$

STEP 8

Now that we have the value of $x$ , we can find the values of the other two integers by substituting $x$ into $x+2$ and $x+4$ .
$x+2 =53+2$ $x+4 =53+4$

STEP 9

Calculate the values of the other two integers.
$x+2 =55$ $x+4 =57$ The three consecutive odd integers are53,55, and57.

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QuestionFind three consecutive odd integers where the sum of the smallest and middle integer equals 51 more than the largest.

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd integers. . The sum of the least and middle integer is51 more than the greatest integer.

STEP 2

Let's denote the three consecutive odd integers as $x$ , $x+2$ , and $x+4$ . The reason we're adding2 each time is because odd numbers are always2 units apart.

STEP 3

According to the problem, the sum of the least integer and the middle integer is51 more than the greatest integer. We can write this as an equation $x + (x+2) = (x+) +51$

STEP 4

implify the equation by combining like terms on each side.
$2x +2 = x +55$

STEP 5

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$x +2 =55$

STEP 6

Subtract2 from both sides of the equation to solve for $x$ .
$x =55 -2$

STEP 7

Calculate the value of $x$ .
$x =53$

STEP 8

Now that we have the value of $x$ , we can find the values of the other two integers by substituting $x$ into $x+2$ and $x+4$ .
$x+2 =53+2$ $x+4 =53+4$

STEP 9

Calculate the values of the other two integers.
$x+2 =55$ $x+4 =57$ The three consecutive odd integers are53,55, and57.

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QuestionFind three consecutive odd integers where the sum of the smallest and middle integer equals 51 more than the largest.

Studdy Solution

STEP 1

Assumptions1. The three integers are consecutive odd integers. . The sum of the least and middle integer is51 more than the greatest integer.

STEP 2

Let's denote the three consecutive odd integers as xxx, x+2x+2x+2, and x+4x+4x+4. The reason we're adding2 each time is because odd numbers are always2 units apart.

STEP 3

According to the problem, the sum of the least integer and the middle integer is51 more than the greatest integer. We can write this as an equationx+(x+2)=(x+)+51x + (x+2) = (x+) +51x+(x+2)=(x+)+51

STEP 4

implify the equation by combining like terms on each side.2x+2=x+552x +2 = x +552x+2=x+55

STEP 5

Subtract xxx from both sides of the equation to isolate xxx on one side.x+2=55x +2 =55x+2=55

STEP 6

Subtract2 from both sides of the equation to solve for xxx.x=55−2x =55 -2x=55−2

STEP 7

Calculate the value of xxx.x=53x =53x=53

STEP 8

Now that we have the value of xxx, we can find the values of the other two integers by substituting xxx into x+2x+2x+2 and x+4x+4x+4.x+2=53+2x+2 =53+2x+2=53+2x+4=53+4x+4 =53+4x+4=53+4

STEP 9

Calculate the values of the other two integers.x+2=55x+2 =55x+2=55x+4=57x+4 =57x+4=57The three consecutive odd integers are53,55, and57.

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Let's denote the three consecutive odd integers as $x$ , $x+2$ , and $x+4$ . The reason we're adding2 each time is because odd numbers are always2 units apart.

According to the problem, the sum of the least integer and the middle integer is51 more than the greatest integer. We can write this as an equation $x + (x+2) = (x+) +51$

implify the equation by combining like terms on each side.
$2x +2 = x +55$

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$x +2 =55$

Subtract2 from both sides of the equation to solve for $x$ .
$x =55 -2$

Calculate the value of $x$ .
$x =53$

Now that we have the value of $x$ , we can find the values of the other two integers by substituting $x$ into $x+2$ and $x+4$ .
$x+2 =53+2$ $x+4 =53+4$

Calculate the values of the other two integers.
$x+2 =55$ $x+4 =57$ The three consecutive odd integers are53,55, and57.