1. ## Finding unknown variables

Two numbers are each multiplied by themselves to give two new numbers. The difference between these two new numbers is less than ten; the difference between the two original numbers was one.
The two original numbers added together was more than 7. What is one of the original numbers?

Let x and y represent the first two numbers

Let a and b represent the two new numbers

xy=ab

a-b < 10

x-y = 1

x + y > 7

Am i on the right path?

What do I do next?

2. ## Re: Finding unknown variables

I think the first sentence means that you have two numbers, say x and y, and they are each squared... this gives you x^2 and y^2 (two "new numbers").

Then x^2 - y^2 < 10
x - y = 1
x + y > 7
Multiply the last two together to get
x^2 - y^2 = (x + y)(x - y) > 7 * 1 = 7

3. ## Re: Finding unknown variables

I'm still at a loss.I don't quite get it.

4. ## Re: Finding unknown variables

Are you aware of the difference of two squares? We have two numbers, $\displaystyle x$ and $\displaystyle y$. We are told they are multiplied by themselves, to give $\displaystyle x^2$ and $\displaystyle y^2$.
We are told then that the difference of the new numbers is less than $\displaystyle 10$, so $\displaystyle x^2-y^2<10$
Using the difference of 2 squares rule,
$\displaystyle (x+y)(x-y)<10$
We are told that the original difference was $\displaystyle 1$, so $\displaystyle x-y=1$
This means that $\displaystyle (x+y)(1)<10$
$\displaystyle (x+y)<10$
We also know that $\displaystyle x+y>7$
This means that
$\displaystyle 7<x+y<10$

Assuming $\displaystyle x$ and $\displaystyle y$ are integers, this doesn't leave many options when $\displaystyle x-y=1$. What are the options?

5. ## Re: Finding unknown variables

We are looking at 4 and 5 ?

6. ## Re: Finding unknown variables

I believe so.