Question

The sum of three consecutive integers is six times of the smallest number. Find the numbers.

Answer 1

Answer:

Examples of three even consecutive integers are: 2,4,6 or 24,26,28

If we choose n to be the smallest, then n+2 and n+4 would be the next two.

"six times the sum of three consecutive even integers"

6(n + n+2 + n+4 )

"is the same as 496 more than 4 times the largest integer"

= 496 + 4( n+4 )

Now that we have an equation, we can solve for n (the smallest of the three):

6(n + n+2 + n+4 ) = 496 + 4( n+4 ) (combine like terms on left side & distribute on right side)

6( 3n + 6 ) = 496 + 4n + 16 (distribute on left & combine like terms on right)

18n + 36 = 512 + 4n (subtract 36 & 4n from both sides)

14n = 476 (divide both sides by 14)

n = 476/14 = 238/7

n = 34

The three consecutive even integers are: {34,36,38}

Check:

6( 34 + 36 + 38 ) = 6(108) = 648

496 + 4(38) = 496 + 152 = 648

Step-by-step explanation:

thank me and mark brainliest

Answer 2

Let the consecutive integers be x,x+1,x+2
So x+x+1+x+2=6x
3x +3 =6x
So 3x=3
X= 1
So numbers are 1,2,3