Find three consecutive even integers such that the sum of the first and second equals 3 times the third.
We have to set up an equation that satisfies this statement.
Notice that consecutive even integers like 2, 4 and 6 , has a common difference of 2 ( such that 4-2 = 2 and 6-4 is also 2 and so on) . We can represent the three consecutive integers by letting:
x - 1st even integer
x + 2 - 2nd even integer
x + 4 - 3rd even integer
It is stated that the sum of the first two integers equals three times the third; the expression that describes this can be written s follows:
x + ( x + 2 ) = 3 ( x + 4)
*sum of the first two integers - x + ( x + 2 )
*three times the third integer - 3 ( x + 4)
Solving for x
x + ( x + 2 ) = 3 ( x + 4)
x + x + 2 = 3x + 12
2x + 2 = 3x + 12
3x - 2x +12 - 2 = 0
x + 10 = 0
x = -10
thus,
x + 2 = -10 + 2 = -8
x + 4 = -10 + 4 = -6
ANSWER:
-10, -8 and -6