Juan invested his savings in two investment funds. The$8000 that he invested in Fund A returned a 1% profit. The amount that he invested in Fund B returned a 5% profit. How much did he invest in Fund B, if both funds together returned a 4% profit?

Question

Juan invested his savings in two investment funds. The$8000  that he invested in Fund A returned a  1% profit. The amount that he invested in Fund B returned a 5% profit. How much did he invest in Fund B, if both funds together returned a 4% profit?

anonymous · Answer

@hero this is the new question they gave me

hero · Answer

a = Fund A = 8000
b = Fund B
c = Total Amount invested

Juan invested 8000 in fund a so:
8000 + b = c

This is the profit equation. He gets a 1% profit return on the 8000 invested in fund a. He gets 5% for fund b, and together he receives 4% profit on the total investment:
.01(8000) + .05b = .04(c)

hero · Answer

So you have to solve this system:

8000 + b = c
.01(8000) + .05b = .04c


Remember:

$1\% = \frac{1}{100} = .01$

$5\% = \frac{5}{100} = .05$

anonymous · Answer

I got b=-1599.2 is that correct

hero · Answer

Nothing will be negative. You can't invest negative money.

hero · Answer

Try to understand the equations first.

anonymous · Answer

6400.8

anonymous · Answer

when I solve for .01(8000) + .05b = .04c it gives me a negative number

hero · Answer

This is a systems of equations. You have to solve both equations together.

anonymous · Answer

im not sure what to do im really confused

hero · Answer

Have you ever solved a system of equations before?

anonymous · Answer

yes the way your telling me to do it Im getting a negative number

anonymous · Answer

I Solve for b first using  .01(8000) + .05b = .04c then I sub B into 8000 + b = c correct

hero · Answer

I haven't told you to do anything yet. I just set up the system. You started doing your own thing.

hero · Answer

What is 1% of 8000?

hero · Answer

That's the same as asking you to simplify .01(8000)

anonymous · Answer

80

hero · Answer

Good. We were able to get that far....so now we have

 8000 + b = c
80 + .05b = .04c

hero · Answer

Now, multiply both sides of the second equation by 100

anonymous · Answer

100(80+.05)=100(.04) correct?

anonymous · Answer

b=0.8c-1600
c=1.25b+2000

hero · Answer

What have you done now? I said to multiply both sides of the second equation by 100, which you did, but you removed the variables...WHY?

hero · Answer

100(80+.05)=100(.04)  <---- not correct

100(80 + .05b) = 100(.04c) <--- is correct

anonymous · Answer

b=1/2000c-0.0006

hero · Answer

You're doing your own thing again...

hero · Answer

Either that or you don't know how to simplify the equation after multiplying both sides by 1000.

anonymous · Answer

I don't know how to

anonymous · Answer

I keep coming up with the wrong answer so I don't know what I am doing

hero · Answer

After multiplying both sides by 100 you get
100(80 + .05b) = 100(.04c)

After simplification you get
8000 + 5b = 4c

hero · Answer

That is still the second equation

hero · Answer

If we put both equations back together again we have

8000 + b = c
8000 + 5b = 4c

hero · Answer

The next thing to do is use substitution since:

c = 8000 + b

Substitute 8000 + b in place of c in the second equation

hero · Answer

Can you do that?

anonymous · Answer

am i solving for b

hero · Answer

Go back to the original question to find out what you're solving for.

anonymous · Answer

24000

hero · Answer

Wow...

hero · Answer

You actually got it

anonymous · Answer

lol

anonymous · Answer

thank you so much

hero · Answer

I see what you were trying to do earlier now. You're solving for b, however, you have to first figure out if you plan to use elimination or substitution to solve the system. If you use elimination, you have to make sure you eliminate variable c. If you use substitution, you have to make sure the final equation you solve is in terms of variable b.

anonymous · Answer

yes I was very confused on what to do but thank you @hero