How to Graph a System of Inequalities for Investment Allocation?

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    Inequalities Systems
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Discussion Overview

The discussion revolves around formulating and graphing a system of inequalities related to investment allocation in two accounts, with constraints on minimum deposits and relative amounts between the accounts. The scope includes mathematical reasoning and conceptual clarification regarding inequalities.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant proposes the inequalities based on the investment constraints: \(x + y \leq 20,000\), \(x \geq 5,000\), and \(y \geq 5,000\).
  • Another participant states that the amount in one account must be at least twice the amount in the other account, suggesting the inequality \(y \geq 2x\).
  • Some participants express skepticism about the need for clarification regarding the inequalities, questioning the understanding of the problem.
  • A later reply emphasizes the importance of distinguishing between the two accounts to correctly apply the inequality \(y \geq 2x\), suggesting that \(y\) should represent the larger account and \(x\) the smaller account.

Areas of Agreement / Disagreement

Participants express differing views on the formulation of the inequalities, with some agreeing on the inequalities proposed while others challenge the clarity and correctness of the definitions used for the accounts. The discussion remains unresolved regarding the best approach to distinguish the accounts and apply the inequalities.

Contextual Notes

There is a lack of consensus on how to define the variables \(x\) and \(y\) in relation to the amounts in the accounts, which affects the interpretation of the inequality \(y \geq 2x\). Additionally, some participants reference unrelated topics, which may distract from the main discussion.

mathland
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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...
 
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mathland said:
The amount in one account is to be at least twice the amount in the other account.

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

Thank you. What information in the problem led you to this inequality?
 
Beer soaked ramblings follow.
skeeter said:
mathland said:
Prove It said:
mathland said:
The amount in one account is to be at least twice the amount in the other account.

$y \geq 2\,x $

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

you’re kidding, right?

https://mathforums.com/threads/systems-of-inequalities.355103/post-640472
https://mathforums.com/threads/systems-of-inequalities.355103/post-640477
Work induced amnesia. Probably. Maybe. Or he just wants a discussion to satisfy his fix for one.
 
mathland said:
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
 
topsquark said:
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.
 
  • #10
mathland said:
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
 
  • #11
topsquark said:
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
 
  • #12
mathland said:
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
 
  • #13
topsquark said:
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.
 
  • #14
Beer soaked non sequitur ramblings follow.
mathland said:
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.
 
  • #15
mathland said:
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
 
  • #16
topsquark said:
It has nothing to do with that. I mistakenly thought I was reading another thread by you is all.

-Dan

Ok.
 
  • #17
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.
 

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