Question

Rachel invested her savings in two investment funds. The amount she invested in Fund A was 4 times as much as the amount she invested in Fund B. Fund A returned a 6% profit and Fund B returned a 5% profit. How much did she invest in Fund B, if the total profit from the two funds together was $3,480?

Answer 1

Alright. So let's call A our investment in Fund A, and B our investment in Fund B. What do we know?

We know that A + B = $3,480. We also know that A is 4 times B. So:

A + B = $3,480.
A = 4B.
4B + B = $3,480.
5B = $3,480.
B = $696.

Now we need to find out how much A is.

A = 4B.
A = 4($696)
A = $2,784.

Now we need to work out our profit. We know that the profit is equal to 6% of our investment in A, and 5% of our investment in B.

Try and figure out the rest from here. If you can't, message me in a few minutes and I'll show you how to calculate the rest.

Answer 2

I don't think A + B = 3480. It said the profit, not the amount invested.

It's probably supposed to be a system of equations. Like
A = 4B
0.06A + 0.05B = 3480
or something.

(Geez, if $3480 is just the profit, this Rachel person is loaded)

Answer 3

wouldnt she have invested $34.80? not unless im doing the work wrong?!.

Answer 4

If she invested $34.80 and made $3480 I want in on this.

But... I think you did the work wrong.

Answer 5

i think everyone would want ins on this lol... its pretty good if you invest a little amount of money and make 10x for the profit

Answer 6

Sacapuntas is right. I'm going to retire for the night, making too many stupid errors. Listen to him/her.

Answer 7

but i would have to use what you got for fund b to multiply it by the 5% profit and the answer i get is $34.80

Answer 8

im not sure if im doing this wrong though.

Answer 9

You're doing it wrong. I can't be more helpful because I don't actually know what you're doing.

Do you understand systems of equations?

Answer 10

not really:/

Answer 11

They actually aren't terribly complicated. You just have more than one equation you have to solve. You have to use them to get down to one variable, and then you can solve that.

For example, here, we know that A = 4B.
So, 0.06A + 0.05B = 3480 can be rewritten as 0.06(4B) + 0.05B = 3480

I assume you know what to do from there!

Answer 12

would the next step be to combine like terms?
for instance add 0.06 and 0.05

Answer 13

Yes. But no.
You have to multiply, first!

Answer 14

oh thats right.
order of operations.

Answer 15

ok so i multiply 0.06 by 4 and get 0.24,
then i add 0.05 to 0.24 qnd get 0.29
then divide?

Answer 16

Yes, it's now a simple matter of getting B by itself.

Answer 17

so the answer i got is $1.20
im not sure if i did that correct.

Answer 18

So now she made $3480 from $1.20. I really, really, really want in on this.

So.. no.

Answer 19

im confused.

Answer 20

You got \[0.29B = 3480\]
So now we want to do
\[B = \frac{3480}{0.29 }\]

Answer 21

i got 12,000

Answer 22

You apparently don't have to find A so that's it.

Answer 23

ok so the answer is that she invested 12,000 in fund B?

Answer 24

You tell me!
Does it make sense? Does it work in the equation?

Answer 25

yes it does thank you very much