word problem help?

Question

find three consecutive even integers such that 6 times the sum of the first and the third is 8 less than 14 times the second. i found the correct answer which is 6, but what formula do i plug that into to find the other two numbers? the book has the answers of 2,4,6

Answer 1

You need to translate the word problem into mathematical equations.

3 consecutive even integers implies:
For some even integer x,
x, x+2, x+4 (as adding an off number to an even number would result in an odd number. Consecutive means the numbers appear one after the other.)

6 times the sum of the first and third is 8 less than 14 times the second.
6*(x + x+4) = 14(x+2) - 8
6*(2x + 4) = 14(x+2) - 8
12x + 24 = 14x + 28 - 8
12x + 24 = 14x + 20
4 = 2x
x = 2

Since the consecutive even integers were defined to be
x, x+2, x+4
and x = 2, the consecutive even integers are
2, 2+2, 2+4, or simply
2, 4, 6

Answer 2

Let the first number be x, therefore the other two numbers are (x +2) and (x +4).
2 and 4 are added to x because the numbers be found are even and consecutive.
By the given condition,
6[x + (x + 4)] = 14(x + 2) - 8
12x + 24 = 14x + 28 - 8
12x + 24 = 14x + 20
-2x +24 = 20
-2x = -4
2x = 4
x = 2
x +2 = 4
x + 4 = 6
Therefore the three numbers are 2,4,6.

Answer 3

Let us name the first even integer α. In such case, the next even integer will be α+2 and the next will be α+4.

Now the formula you gave is:

6*(α + (α+4)) = (14*(α+2)) - 8


Now let us see if our formula works:
6*(α + (α+4)) = (14*(α+2)) - 8
6α + 6α + 24 = 14α + 28 - 8
12α + 24 = 14α + 20
24 - 20 = 14α - 12α
4 = 2α
2α = 4
α = 4/2
α = 2

So the first integer is 2, the second is 2+2 and the third is 2+4 so they are 2, 4 and 6. Let us plug 2 into our original formula and see if it works:

6*(α + (α+4)) = (14*(α+2)) - 8
6 * (2 + (2+4)) = (14 * (2+2)) - 8
6 * 8 = (14* 4) - 8
48 = 56 - 8
48 = 48

We got it!

Good luck.

Answer 4

Let the numbers be x, x+2 and x+4.
The sum of the first and third no is
x+x+4=2x+4
By the problem,
6(2x+4)=14(x+2)-8
=> 12x+24=14x+28-8
=>12x-14x=28-8-24
=> -2x= -4
=>x=2
kTherefore,the nos, are 2,4 and 6

Answer 5

1st number: n
2nd number: n+2
3rd number: n+4

6(n + n+4) = 14(n+2) - 8
12n + 24 = 14n + 20
4 = 2n
n = 2
n+2 = 4
n+4 = 6

Answer 6

let x=1st no.
x+2=2nd no.
x+4=3rd no.

6(x+(x+4))=14(x+2)-8
6(2x+4) = 14x+28-8
12x+24=14x+28-8
14x-12x=24-20
2x=4
x=2

therefore:
(x+2)=2+2=4
(x+4)=2+4=6

Answer 7

welll the equation would be 6(a+c)= 14b-8 does that help if u need anymore help then just ask me