Question 152989
There is NO solution to this problem.
The reason is:
The statement "four consecutive even numbers have a sum that is 10 more than the sum of the smallest two numbers" means the sum of the two largest consecutive numbers is 10. But this is impossible as the sum of two consecutive number is always an odd number.
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You can also explain this by setting up an equation and solving it.
Let the four consecutive number be n-1, n, n+1,n+2(note n is an integer).
As their sum is 10 more than the sum of the smallest two numbers, we can set up an equation:
n-1+n+n+1+n+2 = 10+n-1+n
Solving for n, we have
4n+2 = 2n+9
2n = 7
n = 3.5
But n need to be an integer, so there is no solution to the equation.