SOLUTION: The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers.

Question 27537: The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers.
Found 2 solutions by sdmmadam@yahoo.com, yougan aungamuthu:
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers.
Consecutive even integers differ by 2
Let the required two consequtive even integers be a and a+2
The greater of a and (a+2) ia 6 less than 3 times the lesser.
That is (a+2)is 6 less than 3a
That is 3a - (a+2) = 6
3a - a -2 = 6
(3a-a) = 6 +2
2a = 8
a = 4
The required consecutive even numbers are 4 and 6
Verification:
The greater should be 6 less than 3times the smaller.
3 times the smaller is 3a = 12
And 6 is of course 6 less than 12
Hence our answer is right
Answer by yougan aungamuthu(2) (Show Source): You can put this solution on YOUR website!
Lets write this out in english first
Basically we are told that the bigger integer is 6 less than 3
times the smaller integer. this means that when we subtract 6
from three times the smaller integer we get the bigger integer.

Therefore,
3(smaller integer) - 6 = bigger integer
Let us call the first even integer 2k where k can be any integer (the 2 is necessary to emphasise we are dealing with even numbers since any even number must have a factor of 2).
Since we are dealing with consecutive even integers the bigger number will be 2k+2 (we add 2 since consecutive even numbers differ by 2)
Now we use 3(smaller integer) - 6 = bigger integer
3(2k) - 6 = 2k+2
6k-6=2k+2
4k=8
k=2 which means the numbers are 2(2) and 2(2)+2
i.e 4 and 6
Note: the first number is 2k but k = 2 therefore the number 2(2)
the second number is 2k+2 but k=2 therefore the number is 2(2)+2

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