SOLUTION: Is it possible for four consecutive even numbers to have a sum that is 10 more than the sum of the smallest two numbers? If so, tell how many solution(s) there are. If there are no

Question 152989This question is from textbook Algebra-Structure and Method
: Is it possible for four consecutive even numbers to have a sum that is 10 more than the sum of the smallest two numbers? If so, tell how many solution(s) there are. If there are no solutions, tell why not. This question is from textbook Algebra-Structure and Method

Answer by orca(409) (Show Source): You can put this solution on YOUR website!
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.

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