Question

College Algebra: 3X3 Linear Systems!
Can somebody work this out step-by-step with me? The problem is:

"Stocks, Bonds, and a Mutual Fund: Marita invested a total of $25,000 in stocks, bonds, and a mutual fund. In one year she earned 8% on her stock investment, 10% on her bond investment, and 6% on her mutual fund, with a total return of $1,860. Unfortunately, the amount invested in the mutual fund was twice as large as the amount she invested in the bonds. How much did she invest in each?"

Answer 1

let x be money in stocks
let y be money in bonds
let z be money in mutual

Answer 2

I had the second equation right, but the first and third wrong. I set it that way.

Answer 3

where did you get z=2y?

Answer 4

x+y+z=25000
0,08*x+0.10*y+0.06*z=1860
z=2*(y)

Answer 5

he amount invested in the mutual fund was twice as large as the amount she invested in the bonds.

Answer 6

Ohhh, okay

Answer 7

So I plug 2y back into .08x+.10y+.6z=1860?

Answer 8

0.06*z

Answer 9

Yeah that's what I meant :D

Answer 10

plug z=2y into both equations
x+y+z=25000
0,08*x+0.10*y+0.06*z=1860

Answer 11

you will have an 2 by 2 linear system then, you can solve that same was as yesterday then

Answer 12

you will have an 2 by 2 linear system then, you can solve that same wa* as yesterday then

Answer 13

i give up

Answer 14

spelling is too hard for me obviously

Answer 15

lolx it's okay Dan.
So, my two linear systems are x+3y=25,000 and 0.08x+0.22y=1,860

Answer 16

haha, don't worry. Everyone gets better at it eventually

Answer 17

yes

Answer 18

Wouldn't I make x+3y=25,000 into 3y=25,000-x

Answer 19

Oh wait

Answer 20

wrong

Answer 21

I would make x+3y=25,000 into x=25,000-3y

Answer 22

both work

Answer 23

Let S represent the initial investment in Stocks.
Let B represent the initial investment in Bonds.
Let F represent the initial investment in Mutual Funds.

S + B + F = 25000

.08S + .10B + .06F = 1860

F = 2B

Those are your three equations in three unknowns. I don't know if you are supposed to solve those manually or if you are allowed to use technology.

Using technology, you can see what the results are at:

http://www.wolframalpha.com/input/?i=.08x+%2B+.10y+%2B+.06z+%3D+1860%2C+x+%2B+y+%2B+z+%3D+25000%2C+z+%3D+2y where x is Stocks, y is Bonds, and z if Mutual Funds @Natasha.g.2013

This problem can also be done with one equation but three equations were specified in the problem statement.

Answered on your first post of the problem:

Answer 24

Well I plugged in x=25,000-3y into 0.08x+0.22y=1,860, solved it, and got y=7000

Answer 25

I agree. @Natasha.g.2013

Answer 26

Well, thank you for that Directrix, but I have to write everything out because I won't have a computer do my final exam.

Answer 27

I have the answers in the back of the textbook, but I want to know how to solve word problems step by step.

Answer 28

Thank you to everyone who helped. :)

Answer 29

np!