# Thread: Having trouble

1. ## Having trouble

Here is my problem:
Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbers.
I have many like that and I can't figure them out for anything... I tried searching the web but no luck.

Any help is GREATLY appreciated.

2. Originally Posted by Ryuuko
Here is my problem:

Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbers.
I have many like that and I can't figure them out for anything... I tried searching the web but no luck.

Any help is GREATLY appreciated.
let the smallest be n, then the integers are n, n+1, n+2 and n+3.

The product of the two smallest is n(n+1), and of the two largest is
(n+2)(n+3), so we are told that

n(n+1) = (n+1)(n+3) - 64.

Which is a quadratic in n, you solve this then you have your four numbers.

RonL

Oppsss.. odd integers.. anyway you get the idea

3. Hello, Ryuuko!

Find 4 consecutive odd integers where the product of the two smaller numbers
is 64 less than the product of the two larger numbers.

You're expected to know how to express consecutive odd integers.

Since odd integers "go up by two", if $\displaystyle x$ is the first one,
. . then the next three are: .$\displaystyle x + 2,\:x + 4,\:x + 6$

$\displaystyle \underbrace{\text{Product of smaller two}}\;\;\underbrace{\text{is}}\;\;\underbrace{\te xt{ 64 less than product of larger two}}$

. . . . $\displaystyle x(x + 2)$ . . . . . . $\displaystyle =$ . . . . . $\displaystyle (x + 4)(x + 6) - 64$

There is our equation! . . . Can you finish it now?