Answer: ken invested $3500 in the 8% account.
Step-by-step explanation:
Let x represent the amount invested in the account earning 8% interest.
Let y represent the amount invested in the account earning 12% interest.
Ken invests 6,000 into two accounts one account earns 8% interest and the other earns 12% interest. This means that
x + y = 6000
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
Considering the account earning 8%
I = (x × 8 × 1)/100 = 0.08x
Considering the account earning 12%
I = (y × 12 × 1)/100 = 0.12y
After one year, his total interest earned from the two accounts totaled $580 . This means that
0.08x + 0.12y = 580 - - - - - - - - - - 1
Substituting x = 6000 - y into equation 1, it becomes
0.08(6000 - y) + 0.12y = 580
480 - 0.08y + 0.12y = 580
- 0.08y + 0.12y = 580 - 480
0.04y = 100
y = 100/0.04
y = 2500
x = 6000 - y = 6000 - 2500
x = 3500
