Question

Anyone that can help me out on this one please?


An investor invested a total of $1,100 in two mutual funds. One fund earned a 7% profit while the other earned a 3% profit. If the investor’s total profit was $61, how much was invested in each mutual fund?
The amount that was invested in the mutual fund that earned 7% was?
The amount that was invested in the mutual fund that earned 3% was?

Answer 1

u have a linear system to solve: x for the investment in fund 1, y for ... in fund 2 then
\[ \large \begin{cases}
x+y=1100\\ 0.07x+0.03y=61
\end{cases} \]

Answer 2

I am a beginner and have no idea what i'm doing, could you explain the steps?

Answer 3

ok. but do u understand the equations?
first that!!

Answer 4

Yes, I see how you have them set up, and I think i'm supposed to start with the first one and isolate x first? but I am unsure of what i am doing as a whole. I would appreciate any help.

Answer 5

well first, to get rid of of the decimal numbers u can multiply the 2nd equation by 100 and get
\[ \large 7x+3y=6100 \]
ok?

Answer 6

ok

Answer 7

now isolate x or y (your pick) from the 1st equation.
what do u get?

Answer 8

hello! @teenandtoddlermom

Answer 9

I am here...I am trying to configure it, but I am unsure.

Answer 10

for instance you would get
\[ \large x=1100-y \]
right?

Answer 11

yes

Answer 12

now u can plug this into the second equation.and get
\[ \large 6100=7x+3y=7(1100-y)+3y \]
right?

Answer 13

yes. I am taking notes on what you are explaining.

Answer 14

can u do the algebra on this last equation:
\[ \large 6100=7(1100-y)+3y \]
?

post what u get

Answer 15

ok so ...
7(1100-y)+3
7700-y+3
7700y-3
am I on the right track?

Answer 16

no

Answer 17

:(

Answer 18

u didn't distribute the 7 properly

Answer 19

let's see:
\[ \large 6100=7(1100-y)+3y=7700-7y+3y=7700-4y \]
do u see where your mistake is?

Answer 20

so we now have
\[ \large 6100-7700=-4y \]
\[ \large -1600=-4y \]
\[ \large y=\frac{-1600}{-4}=400 \]
got it?

Answer 21

so that is for my first equation? you plugged it into the second equation?

Answer 22

now plug this into the first equation and find the value of x.
try it!! it is easy

Answer 23

so for the x + y =1100
it's 400=1100

Answer 24

do I subtract them?

Answer 25

or its, x+400=1100?

Answer 26

what happened with the x?

Answer 27

i mean u now know y=400 so
\[ \large 1100=x+y=x+400 \]

Answer 28

so x=700

Answer 29

yes.

Answer 30

7% = 700
and 3% is 400
is this right?

Answer 31

no.

Answer 32

x=700 (what u invest in the 1st fund)
y=400 (what u invest in the 2nd fund)