Math

QuestionFind the equation for the sum of 3 consecutive odd integers equal to -33 and the ratio of the largest to smallest. 2-2-

Studdy Solution

STEP 1

Assumptions1. The integers are consecutive odd numbers. . The sum of the three integers is -33.
3. We need to find the ratio of the largest number to the smallest number.

STEP 2

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

STEP 3

According to the problem, the sum of these three integers is -33. So, we can write the equation asn+(n+2)+(n+)=33n + (n+2) + (n+) = -33

STEP 4

implify the equation by combining like terms.
3n+6=333n +6 = -33

STEP 5

Subtract from both sides of the equation to isolate 3n3n on one side.
3n=333n = -33 -

STEP 6

Calculate the right side of the equation.
3n=393n = -39

STEP 7

Divide both sides of the equation by3 to solve for nn.
n=39/3n = -39 /3

STEP 8

Calculate the value of nn.
n=13n = -13

STEP 9

Now that we have the value of nn, we can find the other two integers by substituting nn into n+2n+2 and n+4n+4.

STEP 10

Calculate the second integer.
n+2=13+2n+2 = -13 +2

STEP 11

Calculate the value of the second integer.
n+=11n+ = -11

STEP 12

Calculate the third integer.
n+4=+4n+4 = - +4

STEP 13

Calculate the value of the third integer.
n+=9n+ = -9

STEP 14

The three consecutive odd integers are -13, -11, and -9. We need to find the ratio of the largest number to the smallest number.

STEP 15

Write the ratio of the largest number to the smallest number as a fraction.
Ratio=Largestnumber/SmallestnumberRatio = Largest\, number / Smallest\, number

STEP 16

Substitute the values of the largest and smallest numbers into the ratio.
Ratio=9/13Ratio = -9 / -13

STEP 17

implify the ratio to its lowest terms.
Ratio=9/13Ratio =9 /13The ratio of the largest number to the smallest number is913.

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