Question 100490: Jon invested a total of $12,000 in stocks, bonds, and mutual funds. She Received a 10% return on her stock investment, an 8% return on her bond investment, and a 12% on her mutual fund. Her total return was $1,230. If the total investment in stocks and bonds equaled her mutual fund investment, then how did she invest in each?
Found 2 solutions by ptaylor, edjones:
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=her stock investment
(1) 0.10x=return on her stock investment
And y=her bond investment
(2) 0.08y=return on her bond investment
Now we are told that (x+y)=her mutual fund investment
(3) 0.12(x+y)=return on her mutual fund investment
Now we know that x+y+(x+y)=12,000--------------------------eq1
We also know that:
(1)+(2)+(3)=1230 or
0.10x+0.08y+0.12(x+y)=1230--------------------------------eq2
simplifying eq1, we get:
2x+2y=12,000 or divide both sides by 2
x+y=6000-------------------------------------------eq1
Simplifying eq2, we get:
0.10x+0.08y+0.12x+0.12y=1230 collect like terms
0.22x+0.20y=1230 divide both sides by 2
0.11x+0.10y=615-------------------------------------------eq2
Multiply eq2 by 10:
1.1x+y=6150----------------subtract this from eq1
-0.1x=-150 divide both sides by -0.1
x=$1500--------------------------------------------amt invested in stocks
From eq1:
1500+y=6000 subtract 1500 from both sides
1500-1500+y=6000-1500
y=$4500---------------------------------------amt invested in bonds
(x+y)=$1500+$4500=$6000----------------------amt invested in mutual funds
CK
$1500+$4500+$6000=$12000
$12000=12000
also
stocks+bonds=mutual funds
1500+4500=6000
6000=6000
As you probably know, we could solve this using three equations and three unknowns, as follows:
Let x=stock investment
y=bond investment
z=mutual fund investment
Our three equations would be:
x+y+z=12000------------------eq1
0.10x+0.08y+0.12z=1230-------eq2
z=x+y---------------------------eq3
Hope this helps----ptaylor
Answer by edjones(8007)  (Show Source):
You can put this solution on YOUR website! She has 6000 in money market yielding 6000*.12=720.
let s= amount in stocks, 6000-s amount in bonds
.1s+.08(6000-s)=510
.1s+480-.08s=510
.02s+480=510
.02s=30
s=1500
bonds=4500
Check
1500*.1=150
4500*.08=360
-------------
========>510
she invested 6000 in mutual funds, 4500 in bonds and 1500 in stocks.
Ed
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