the sum of 5 consecutive numbers is half the middle number multiplied by 10.

5 consecutive numbers can be represented by: N, N+1, N+2, N+3, N+4.

So we have:

(N) + (N+1) + (N+2) + (N+3) + (N+4) = 1/2(N+2)*10

5N + 1 + 2 + 3 + 4 = (1/2N +1)*10

5N + 10 = 5N + 10

5N = 5N

N = N

 

I believe this is saying that N could be any number, because we couldn't solve for it.

Let's check this by putting some random numbers for N in to the equation:

 

N = 10

(N) + (N+1) + (N+2) + (N+3) + (N+4) = 1/2(N+2)*10

((10)) + ((10)+1) + ((10)+2) + ((10)+3) + ((10)+4) = 1/2((10)+2)*10

10 + 11 + 12 + 13 + 14 = 1/2(12)*10

60 = 6*10

60 = 60

 

N = -7

(N) + (N+1) + (N+2) + (N+3) + (N+4) = 1/2(N+2)*10

((-7)) + ((-7)+1) + ((-7)+2) + ((-7)+3) + ((-7)+4) = 1/2((-7)+2)*10

(-7) + (-6) + (-5) + (-4) + (-3) = 1/2(-5)*10

-25 = (-5/2)*10

-25 = -50/2

-25 = -25