# Systems of Inequalities

• MHB
mathland
A person plans to invest up to 20,000 dollars in two different interest-bearing accounts. Each account must contain at least 5,000 dollars. The amount in one account is to be at least twice the amount in the other account. Write and graph a system of inequalities that describes the various amounts that can be deposited in each account.

Solution:

Let x = first account

Let y = second account

The words "up to" tells me to use less than or equal to when adding the two accounts.

The words "at least" tells me to use greater than or equal to as a second inequality in the system.

One of the inequalities is x + y < = 20,000.
I think the following two inequalities are also part of the systems of inequalities I must find:

x >= 5,000

y >= 5,000

I somehow think there is one more inequality missing. Stuck here...

Gold Member
MHB
The amount in one account is to be at least twice the amount in the other account.

$y \geq 2\,x$

jonah1
Beer soaked ramblings follow.
$y \geq 2\,x$
You should have just let him figure that out for himself.
He'll be back for more.

mathland
$y \geq 2\,x$

Thank you. What information in the problem led you to this inequality?

jonah1
mathland

Wish I was but no pun intended.

Gold Member
MHB
Thank you. What information in the problem led you to this inequality?
It astounds me that you had to ask this question when you recently posted about that quintic equation. Try to stick to one level of Mathematics. Learning works better that way.

-Dan

mathland
It astounds me that you had to ask this question when you recently posted about that quintic equation. Try to stick to one level of Mathematics. Learning works better that way.

-Dan

I found the quintic equation on FB. I had no idea the actual question is beyond precalculus.

Gold Member
MHB
I found the quintic equation on FB. I had no idea the actual question is beyond precalculus.
Just out of curiosity...

There is no general formula for a quintic. Can you post what you found?

-Dan

mathland
Just out of curiosity...

There is no general formula for a quintic. Can you post what you found?

-Dan

The original question was removed from the math group.

Here it is:

Solve for x∈ℤ.

x^5-15x^3-x-60 = 0

Gold Member
MHB
The original question was removed from the math group.

Here it is:

Solve for x∈ℤ.

x^5-15x^3-x-60 = 0
Oh. Okay. You already posted that problem elsewhere. Thanks.

-Dan

mathland
Oh. Okay. You already posted that problem elsewhere. Thanks.

-Dan

I am not going to post so many problems. I can see that it does not matter if I show my work or not. Members do not want me to bombard the site with math questions in a MATH FORUM.

jonah1
Beer soaked non sequitur ramblings follow.
I am not going to post so many problems. I can see that it does not matter if I show my work or not. Members do not want me to bombard the site with math questions in a MATH FORUM.
I should join an aerobics class.

Gold Member
MHB
I am not going to post so many problems. I can see that it does not matter if I show my work or not. Members do not want me to bombard the site with math questions in a MATH FORUM.
It has nothing to do with that. I mistakenly thought I was reading another thread by you is all.

-Dan

mathland
It has nothing to do with that. I mistakenly thought I was reading another thread by you is all.

-Dan

Ok.

HOI
The problem I have is that the first post defines x and y by
"Let x = first account

Let y = second account"
without saying how to distinguish the "first account" from the "second account".

That is especially important because of the condition that "The amount in one account is to be at least twice the amount in the other account." THAT is what we need to distinguish the two accounts.

I would have said "Let y be the amount in the LARGER account and let x be the amount in the SMALLER account".

That is what we need to establish that $$y\ge 2x$$, not $$x\ge 2y$$.