Help with this question please

ge0rge · 2012-01-07 03:24:16

The product of two numbers is 999
The difference between them is 10
What are the two numbers?

What is the method to arrive at the answer?

Thanks in advance

anonimnystefy · 2012-01-07 04:30:50

hi ge0rge

here's one way:

we have:
a*b=999

and

a-b=10

from the second we can write that a=b+10

when we substitute into the first equation we get:

(b+10)*b=999
b^2+10b-999=0

now solve this like a quadratic.you should get two values for b.when you substitute them back in a=b+10 you will get the corresponding two values for a.

bobbym · 2012-01-07 08:07:36

Hi ge0rge;

anonimnystefy has given you the preferred way to solve that. Here is another way. If you factor 999 you will get.

Which is 27 * 37, this is your answer.

anonimnystefy · 2012-01-07 08:20:55

hi bobbym

yes guessing can often be more effective,but may not always work and the solution may not always be easy to spot.

bobbym · 2012-01-07 08:23:24

Hi anonimnystefy;

Your back, good to see you. I did not guess, factoring in this case is a systematic way to get there.

anonimnystefy · 2012-01-07 08:27:12

hi

well maybe,but the other one is more elegant and demands less trying out.

bobbym · 2012-01-07 08:28:52

Hi;

Depends on your definition of elegance. Also, supposing a person does not know any algebra?

anonimnystefy · 2012-01-07 08:42:11

hi

that's assuming the common definition of elegance and assuming that a person possesses some knowledge in algebra.if they don't i propose they don't do this kinds of problems.

bobbym · 2012-01-07 08:48:31

Hi anonimnystefy;

Elegance is a synonym for beauty that has come to acquire the additional connotations of unusual effectiveness and simplicity

Now how do we define simplicity and effectiveness in mathematics?

if they don't i propose they don't do this kinds of problems.

Supposing they do not want to follow your proposal? Many people think about math problems even before they learn any mathematics at all.

ge0rge · 2012-01-07 22:30:36

Thank you for your help.

I guess I am asking for help with quadratic equations now. Also I dont understand why I would get two answers for a and b, anonimnystefy.

bobbym · 2012-01-07 22:42:08

Hi ge0rge;

Because using the algebraic way ( anonimnystefy's post ) you will see that there are two sets of solutions,

-27 and - 37
and
27 and 37

ge0rge · 2012-01-07 22:56:54

thanks bobby so can you show me how the quadratic equation gets the answer please.
(b+10)*b=999
b^2+10b-999=0

george aged 10

bobbym · 2012-01-07 23:06:07

Hi;

It is done by algebra.

We can now factor the equation or use the quadratic formula. Let's factor.

So we have b = 27 and b = - 37, now you would substitute back into a-b =10 to get the full answers.

I admire the fact that you are only 10 and trying to understand that. If you understand it that is good. If not, please do not get discouraged. It will all be clear to you soon.

In the meantime look at my solution for a way to do it without the algebra. Keeping in mind that anonimnystefy's way is the preferred one.

Also, I hope you will become a steady member of the forum, see you later.

Math Is Fun Forum

#1 2012-01-07 03:24:16

Help with this question please

#2 2012-01-07 04:30:50

Re: Help with this question please

#3 2012-01-07 08:07:36

Re: Help with this question please

#4 2012-01-07 08:20:55

Re: Help with this question please

#5 2012-01-07 08:23:24

Re: Help with this question please

#6 2012-01-07 08:27:12

Re: Help with this question please

#7 2012-01-07 08:28:52

Re: Help with this question please

#8 2012-01-07 08:42:11

Re: Help with this question please

#9 2012-01-07 08:48:31

Re: Help with this question please

#10 2012-01-07 22:30:36

Re: Help with this question please

#11 2012-01-07 22:42:08

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#12 2012-01-07 22:56:54

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#13 2012-01-07 23:06:07

Re: Help with this question please

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