Systems of Linear Equations in Applications: "Pierre inherited $120,000 from...."

N

NoGoodAtMath

New member
Joined
May 2, 2013
Messages
35
Systems of Linear Equations in Applications: "Pierre inherited $120,000 from...."

First here this the application: Pierre inherited $120,000 from his uncle and decided to invest the money. He put part of the money in a money market account that earns 2.2% simple interest. The remaining money was invested in a stock that returned 6% in the first year and a mutual fund that lost 2% in the first year. he invested $10,000 more in the stock than in the mutual fund, and his net gain for 1 year was $2820. Determine the amount invested in each account.

So here's how I set up the equations.

x+y+z=120,000
-x+y-z=10,000
22x+60y-20z=2820

From there I worked everything out, but kept getting decimals. Then I switched the amounts 120,000 and 2820 and the answers still didn't come out correct. What did I do wrong setting up the equations?
 
NoGoodAtMath said:
First here this the application: Pierre inherited $120,000 from his uncle and decided to invest the money. He put part of the money in a money market account that earns 2.2% simple interest. The remaining money was invested in a stock that returned 6% in the first year and a mutual fund that lost 2% in the first year. he invested $10,000 more in the stock than in the mutual fund, and his net gain for 1 year was $2820. Determine the amount invested in each account.

So here's how I set up the equations.

x+y+z=120,000
-x+y-z=10,000
22x+60y-20z=2820

From there I worked everything out, but kept getting decimals. Then I switched the amounts 120,000 and 2820 and the answers still didn't come out correct. What did I do wrong setting up the equations?
Click to expand...

How can ANYONE understand what you wrote if you do not define your variables.

Although I think it is rude for me to define your variable (since I might be wrong) I will do my best, so I can help you.

x= am't invested in money market
y= am't invested in stocks
z= am't invested in mutual funds

Your first equation is correct
Your 2nd equation: You were giving information that involved only y and z, yet your equation involved x, y and z.
Equation 3: 6% is NOT 60, 2% is not 20 and 2.2% is not; 22 BUT 2820 is 2820.
 
Last edited:
NoGoodAtMath said:
First here this the application: Pierre inherited $120,000 from his uncle and decided to invest the money. He put part of the money in a money market account that earns 2.2% simple interest. The remaining money was invested in a stock that returned 6% in the first year and a mutual fund that lost 2% in the first year. he invested $10,000 more in the stock than in the mutual fund, and his net gain for 1 year was $2820. Determine the amount invested in each account.

So here's how I set up the equations.

x+y+z=120,000
-x+y-z=10,000
22x+60y-20z=2820

From there I worked everything out, but kept getting decimals. Then I switched the amounts 120,000 and 2820 and the answers still didn't come out correct. What did I do wrong setting up the equations?
Click to expand...
.
Let:

The amount of money invested in Money Market = M

The amount of money invested in Stock = S

The amount of money invested in mutual Fund = F

Those equations should be:

M + S + F = 120,000

S - F =10000

0.022*M + 0.06*S - 0.02*F = 2820
 
Last edited by a moderator:
Denis said:
a = money market
b = stocks
c = mutual funds (I simply hate z as a variable!)

a + b + c = 120000 [1]
b - c = 10000 [2]
22a + 60b - 20c = 2820000 [3] (NOT 2820)

3 equations, 3 unknowns.
Go to town!
Hint: start by adding [1] + [2]

NOTE: Jomo's in a bad mood cause his speech
time has been cut to 10 minutes...:rolleyes:
Click to expand...


10 minutes :( :confused: :mad:
 
Systems of Linear Equations in Applications

Denis said:
a = money market
b = stocks
c = mutual funds (I simply hate z as a variable!)

a + b + c = 120000 [1]
b - c = 10000 [2]
22a + 60b - 20c = 2820000 [3] (NOT 2820)

3 equations, 3 unknowns.
Go to town!
Hint: start by adding [1] + [2]

NOTE: Jomo's in a bad mood cause his speech
time has been cut to 10 minutes...:rolleyes:
Click to expand...

Thanks for taking the time to correct my mistakes, and I apologize for not setting up my variables. I hope you had a good day. Now I'm going to try to solve this application. I'm not good with them.
 
Jomo said:
How can ANYONE understand what you wrote if you do not define your variables.

Although I think it is rude for me to define your variable (since I might be wrong) I will do my best, so I can help you.

x= am't invested in money market
y= am't invested in stocks
z= am't invested in mutual funds

Your first equation is correct
Your 2nd equation: You were giving information that involved only y and z, yet your equation involved x, y and z.
Equation 3: 6% is NOT 60, 2% is not 20 and 2.2% is not; 22 BUT 2820 is 2820.
Click to expand...

Thank you for responding.
 
Subhotosh Khan said:
.
Let:

The amount of money invested in Money Market = M

The amount of money invested in Stock = S

The amount of money invested in mutual Fund = F

Those equations should be:

M + S + F = 120,000

S - F =10000

0.022*M + 0.06*S - 0.02*z = 2820
Click to expand...

Thank you for responding, I really appreciate it. I'm not good with word problems.
 
NoGoodAtMath said:
Thank you for responding.
Click to expand...
Can you show us your work so we can confirm that you have the correct answer? Also, if you keep thinking/writing/saying that you are not good at word problems you probably will not be good at word problems. Just do many of them and ask us here at the forum for help.
 
Jomo said:
Can you show us your work so we can confirm that you have the correct answer? Also, if you keep thinking/writing/saying that you are not good at word problems you probably will not be good at word problems. Just do many of them and ask us here at the forum for help.
Click to expand...

I sure can.

[A]= Money Market
= Stocks
[C]= mutual fund

I added A and B and got this a+b+c= 120,000
b-c= 10,000
-------------------
a+2b= 130,000

(20) a+b+c= 120,000
22a+60b-20c= 2,820,000 that gets me 20a+20b+20c= 2,400,000
22a+60b-20c= 2,820,000
--------------------------------
42a+80b= 5,220,000

(-42) a+2b= 130,000
42a+80b= 5,220,000 -------> -42a-84b= -5460000
42a+80b=5220000
----------------------------
-4b= -24,0000 then I divided by -4 to get b=60,000

a+2(60,000)= 130,000--------------> a+120,000= 130,000----------> a=10,000

10,000+60,000+c= 120,000-----> 70,000+c= 120,000----> c=50,000
So, Pierre invested $10,000 in the money market, $60,000 in stocks and $50,000 in the mutual fund.
 
You must log in or register to reply here.
Top