SEVEN TIMES THE SUM OF THREE CONSECUTIVE EVEN INTEGERS IS 140 MORE THAN ELEVEN TIMES THE MIDDLE INTEGER. FIND THE INTEGERS

Answer

No solution.

Let x be the first even integer.
Then the next two consecutive even integers are x + 2 and x + 4.
The sum of these three integers is 3x + 6.
Seven times the sum is 21x + 42.
Let y be the middle integer, or x + 2.
Eleven times the middle integer is 11y = 11(x + 2) = 11x + 22.
Seven times the sum is 140 more than eleven times the middle integer: 21x + 42 = 11x + 22 + 140.
Simplifying the equation, we get 10x = 76.
Therefore, the first even integer is x = 7.6, which is not an integer, so there is no solution to the problem.