# Thread: Finding the minimum product of two numbers whose difference is 8, HOW?

1. ## Finding the minimum product of two numbers whose difference is 8, HOW?

Finding the minimum product of two numbers whose difference is 8, HOW?

This is the solution in my textbook:

"The quantity to be minimized is the product, p, of two numbers.
Let one number be n.
Since the difference between the two numbers is 8, the other number can be represented by n-8 or n+8.
Either expression can be used. We will use n-8.
p = n * (n-8)
...
"

Now the thing I don't get is that why do we need P? Why do we multiply the two numbers?

2. Originally Posted by Sorena
This is the solution in my textbook:

"The quantity to be minimized is the product, p, of two numbers.
Let one number be n.
Since the difference between the two numbers is 8, the other number can be represented by n-8 or n+8.
Either expression can be used. We will use n-8.
p = n * (n-8)
...
"

Now the thing I don't get is that why do we need P? Why do we multiply the two numbers?
what is the definition of the word "product"?

3. Originally Posted by skeeter
what is the definition of the word "product"?
You may find it hard to believe, skeeter, but I have had classes full of college students who would have trouble answering your question. To them a "product" is something advertised on TV and has nothing to do with mathematics!

4. ok, so what does it mean?

5. well i kinda know it means the multiple of the 2 numbers, the thing I don't understand is that why we need to get that? how does that help?

6. Originally Posted by Sorena
well i kinda know it means the multiple of the 2 numbers, the thing I don't understand is that why we need to get that? how does that help?
The question was
Finding the minimum product of two numbers whose difference is 8
Given the question, I don't understand why you would not understand the importance of getting the product!

7. Originally Posted by Sorena
well i kinda know it means the multiple of the 2 numbers, the thing I don't understand is that why we need to get that? how does that help?
the problem wants you to find the minimum product of two numbers whose difference is 8

the product of two numbers is the result when you multiply the two numbers ...

the product = (first number) times (the second number)

P = n(n-8)

note that the graph of P = n(n-8) is a parabola ... the vertex of the parabola is the location of the minimum product.

what do you know about finding the vertex of a parabolic graph?

8. LOL, I didn't even read the question properly, their difference was in my mind, thanks for the help though.

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### two numbers have a difference of 8 and their product is a minimum

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