There are 5 consecutive even integers the sum of the first two numbers is 78 less than the sum of the last three numbers what are the integers?

Let's call the third number X.

The first number is X-4

The second is X - 2

The fourth is X + 2

The fifth is X + 4

So now what do we know about these numbers?

Well they all add up to 5X

and

(X - 4) + (X - 2) + 78 = X + (X + 2) + (X + 4)

Add the Xs

2X - 6 + 78 = 3X + 6

Subtract the 6 from the right-hand side

2X - 6 + 78 - 6 = 3X

Simplify the numbers

2X + 66 = 3X

Subtract the 2X from the left-hand side

66 = 3X - 2X

66 = X

Now we can see that

The first number is 62

The second is 64

The third is 66

The fourth is 68

The fifth is 70

and

62 + 64 = 126

and

66 + 68 + 70 = 204

and

126 + 78 = 204