Math

QuestionFind three consecutive odd integers where the sum of the first two equals five times the largest plus three.

Studdy Solution

STEP 1

Assumptions1. The three numbers are consecutive odd integers. . The sum of the smaller two numbers is equal to five times the largest number increased by three.

STEP 2

Let's denote the three consecutive odd integers as xx, x+2x+2, and x+4x+4. We use x+2x+2 and x+4x+4 because odd integers are always2 units apart.

STEP 3

According to the problem, the sum of the first two integers is equal to five times the third integer increased by three. We can express this as an equationx+(x+2)=5(x+)+3x + (x+2) =5(x+) +3

STEP 4

implify the left side of the equation by combining like terms2x+2=x+20+32x +2 =x +20 +3

STEP 5

Further simplify the right side of the equation2x+2=5x+232x +2 =5x +23

STEP 6

To solve for xx, we need to isolate xx on one side of the equation. Let's subtract 2x2x from both sides2=3x+232 =3x +23

STEP 7

Now, subtract23 from both sides to isolate xx21=3x-21 =3x

STEP 8

Finally, divide both sides by3 to solve for xxx=7x = -7

STEP 9

Now that we have the value of xx, we can find the three consecutive odd integers. They are xx, x+2x+2, and x+4x+4.

STEP 10

Substitute x=7x = -7 into the expressions for the three integersThe first integer is x=7x = -7.
The second integer is x+2=7+2=5x+2 = -7 +2 = -5.
The third integer is x+4=7+4=3x+4 = -7 +4 = -3.
The three consecutive odd integers are -7, -5, and -3.

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