Question

an investor invested a total of 3,100 in two mutual funds. One fund earned a 6% profit while the other earned a 2% profit. If the investors total profit was $110 how much was invested in each mutual year.

Answer 1

Let the amounts invested be A and B.
The following equations can be set up from the given information:
A + B = 3100 ........(1)
0.06A + 0.02B = 110 .........(2)
We can find B in terms of A from equation (1) by rearrangement:
B = 3100 - A .............(3)
If you plug the expression for B given by (3) into equation (2) you can get an equation that can be solved to find the value of A.
Can you do that?

Answer 2

so it would be 3100*0.02+110

Answer 3

0.06A + 0.02(3100 - A) = 110
0.06A + 0.02 * 3100 - 0.02A = 110 ..........(4)

Answer 4

so I can get 2 separate answers wouldn't it be 0.06*3100 but where would the 110 fit in?

Answer 5

There is only one answer for A:
0.06A + 0.02 * 3100 - 0.02A = 110 ..........(4)
Gathering like terms in (4) gives:
0.06A - 0.02A + 0.02 * 3100 = 110 ........(5)
Simplifying (5) gives:
0.04A + 62 = 110 .............(6)
Now if you subtract 62 from the left hand side of (6) and subtract 62 from the right hand side of (6) what do you get?

Answer 6

the way the answers are set up it wants to know the profit of 6% and then the profit of 2% underneath

Answer 7

Amount A earns 6% and amount B earns 2%. You can see that from equation (2) in my first post.
So now can you do the following to enable amount A to be found?
0.04A + 62 = 110 .............(6)
If you subtract 62 from the left hand side of (6) and subtract 62 from the right hand side of (6) what do you get?

Answer 8

After amount A is found, amount B can be found by pugging amount A into equation (1).

Answer 9

The question that you have posted asks for the amounts invested, which are A and B.

Answer 10

so a=48 im confused now

Answer 11

No. Your value for A is incorrect.
0.04A + 62 = 110 .............(6)
Subtracting 62 from both sides of (6) gives
0.04A + 62 - 62 = 110 - 62 ..........(7)
Simplifying (7) gives
0.04A = 48 ............(8)
Now divide both sides of (8) by 0.04 to find the value of A.

Answer 12

0.04A = 48 ............(8)
\[\frac{0.04A}{0.04}=A=\frac{48}{0.04}=you\ can\ calculate\]

Answer 13

a=1200
b=

Answer 14

Correct! Amount A that earns 6% is $1200. Now plug that value for A into equation (1) to find the amount B:
A + B = 3100 ........(1)
1200 + B = 3100 ...........(9)
Now subtract 1200 from both sides of (9).

Answer 15

b=1900

Answer 16

Correct! Amount A earning 6% is $1200 and amount B earning 2% is $1900.

Answer 17

thx

Answer 18

You're welcome :)