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?

Answer 1

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