How to Graph a System of Inequalities for Investment Allocation?

In summary, the first account can contain up to 20,000 dollars, but the second account cannot contain more than 5,000 dollars.
  • #1
mathland
33
0
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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  • #2
mathland said:
The amount in one account is to be at least twice the amount in the other account.

$y \geq 2\,x $
 
  • #3
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.
 
  • #4
Prove It said:
$y \geq 2\,x $

Thank you. What information in the problem led you to this inequality?
 
  • #6
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.
 
  • #8
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
 
  • #9
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 [tex]y\ge 2x[/tex], not [tex]x\ge 2y[/tex].
 

What is a system of inequalities?

A system of inequalities is a set of two or more inequalities that are graphed on the same coordinate plane. The solution to the system is the region where all of the inequalities overlap.

How do you graph a system of inequalities?

To graph a system of inequalities, you first graph each individual inequality on the same coordinate plane. Then, you shade in the region where all of the inequalities overlap. This shaded region represents the solution to the system.

What is the difference between a system of inequalities and a system of equations?

A system of inequalities involves inequalities (>, <, ≥, ≤) while a system of equations involves equations (=). In a system of inequalities, the solution is a region on the coordinate plane, while in a system of equations, the solution is a specific point or set of points.

How do you solve a system of inequalities?

To solve a system of inequalities, you need to find the values that make all of the inequalities true. This can be done by graphing the system and finding the overlapping region, or by using algebraic methods such as substitution or elimination.

What are some real-life applications of systems of inequalities?

Systems of inequalities can be used to represent and solve real-life problems involving constraints. For example, a company may use a system of inequalities to determine the optimal production levels for different products based on limited resources. They can also be used in economics to model supply and demand, or in urban planning to determine the best locations for resources such as schools or hospitals.

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