SOLUTION: Find four consecutive even integers such that three times the sum of the first and third numbers is equal to four times the sum of the second and fourth numbers.

Question 1173273: Find four consecutive even integers such that three times the sum of the first
and third numbers is equal to four times the sum of the second and fourth
numbers.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
Find four consecutive even integers...

the first number, the smallest, even integer = x

the second number, the next to smallest, even integer = x+2

the third number, the next to largest, even integer = x+4

the fourth number, the largest even integer = x+6

the sum of the first and third numbers = x+(x+4) = x+x+4 = 2x+4 

the sum of the second and fourth numbers. (x+2)+(x+6) = x+2+x+6 = 2x+8

...three times the sum of the first and third numbers is equal to
four times the sum of the second and fourth numbers.


3(2x+4) = 4(2x+8)
  6x+12 = 8x+32
    -2x = 20
      x = -10

So,

he first number, the smallest, even integer = -10

the second number, the next to smallest, even integer = -8

the third number, the next to largest, even integer = -6

the fourth number, the largest even integer = -4

Answer: 10, -8, -6, -4.

Checking: 

the sum of the first and third numbers = (-10)+(-6) = -16 
 
the sum of the second and fourth numbers = (-8)+(-4) = -12

It's true that 3 times -16 which is -48, is equal 
to 4 times -12, which is also -48.

Edwin

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