Question

Find 4 consecutive even integers where the product of the two smaller numbers is 56 less than the product of the two larger numbers.

Answer 1

Let 'x' be the smallest of the integers.
Then, the next 3 integers will be (x+2), (x+4), and (x+6).

The product of the two smaller numbers is 56 LESS than the product of the 2 larger.

\[x(x+2) + 56 = (x+4)(x+6)\]
Does that seem right? Set it up as an equation.

Answer 2

I wish I could tell you if that seemed right, but I have no idea... which is why I am here :D you might have to keep going step by step to help me understand because integers are my weakness. x_x

Answer 3

An integer is a positive or negative "whole number". So, 3, 92, -235, and 0 are all integers.

Answer 4

Okay. Got that part. Now what?

Answer 5

Apparently, 0 may or may not be an integer. >_> But whatever. We don't have to deal with 0.
So, we need 4 consecutive even integers. We'll let the smallest of the integers be x.

Answer 6

And, the next consecutive even integer, you must add 2 to it. Like, 2, 4, 6, etc. You have to add 2.
So, x is the smallest integer. The next smallest is (x+2). The next, (x+4). And finally, the biggest is (x+6).

Answer 7

Okay I see the 4 integers but why are we adding 2 to each one?

Answer 8

Because that's what makes them both even and consecutive. Another example.
Let x = 10.
(10 + 2) = 12
(10 + 4) = 14
(10 + 6) = 16
10, 12, 14, 16 are all even, consecutive integers.

Answer 9

Oh, duh... -Facepalm- I'm so dumb -_-

Answer 10

It's kewl. :3
Now, we move on to creating our equation for 'the product of the two smaller numbers is 56 less than the product of the two larger numbers.'

Answer 11

'The product of the two smaller numbers' : x(x+2)
'the product of the two larger numbers' : (x+4)(x+6)
Since the product of the smaller numbers is 56 less than the bigger product, we'll have to add 56 to the smaller product to make them equal.

\[x(x+2) + 56 = (x+4)(x+6)\]

Answer 12

Okay, I'm following.

Answer 13

Do I solve that equation and it gives me the answer or is there more to it?

Answer 14

Yes, solve the equation for x. It'll be a quadratic equation. Use the even integer for x. Then, you can find the consecutive, even integers. Remember, we already said that 'x' equals the smallest of the even integers.

Answer 15

@iPwnBunnies

Answer 16

Oh, wut. You already told me what you did in chat.
Yas, x = 4.
Therefore, the next 3 consecutive integers are 6, 8 and 10.
Check your work.

\[(4)(6) + 56 = (8)(10) ?\]

Answer 17

It does not equal that D;

Answer 18

.-. I'm confused now. Your answer to the original question is correct, lol.