An investor invested a total of $2,100 in two mutual funds.

Question

One fund earned a 6% profit while the other earned a 2% profit. If the investor's total profit was $74, how much was invested in each mutual fund?

The amount invested in the mutual fund that earned 6% was what in dollars?

The amount invested in the mutual fund that earned 2% was what in dollars?

Answer 1

let x be amount invested at 6% and y be the amount invested at 2%.

.06x + .02y = 74       eq. (1)

x + y = 2100            eq. (2)

we are going to do a substitution:

y = 2100 - x             eq. (3)

substitute y from eq. (3) to eq. (1):

.06x + .02 * (2100 - x) = 74

.06x +  42 - .02x = 74

.04x = 74 -42

.04x = 32

.04x/.04 = 32 / .04

x = 800

y = 2100 - 800 = 1,300

so, amount invested at 6% is $800, and $1,300 at 2%

 

 

 

Answer 2

$(x) invested into 6% ... funds
$(y)      .......       2%     ...... 

(1) ...  x + y = 2100   --->  x = 2100 - y
(2) ... 0.06x + 0.02y = 74
0.06(2100 - y) + 0.02y = 74
126 - 0.06y + 0.02y = 74
-0.04y = 74 - 126 ---> -0.04y = -52 ---> y = -52 / -0.04 
y = 1300
x = 800
Check:
$800 + $1300 = $2100
0.06 · 800 + 0.02 · 1300 = 74
       ↓                 ↓
      48      +       26