Answer:$4000 was invested into the account earning 6% interest.
$2000 was invested into the account earning 11% interest.
Step-by-step explanation:
Let x represent the amount invested into the account earning 6% interest.
Let y represent the amount invested into the account earning 11% interest.
Mike has $6000 to invest. He invested part of his total into an account earning 6% interest and the rest in an account earning 11% 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 6% interest, the interest would be
I = (x × 6 × 1)/100 = 0.06x
Considering the account earning 11% interest, the interest would be
I = (x × 11 × 1)/100 = 0.11y
If at the end of the year, he earned $460.00 in interest, it means that
0.06x + 0.11y = 460 - - - - - - - - - - -1
Substituting x = 6000 - y into equation 1, it becomes
0.06(6000 - y) + 0.11y = 460
360 - 0.06y + 0.11y = 460
- 0.06y + 0.11y = 460 - 360
0.05y = 100
y = 100/0.05 = $2000
x = 6000 - y = 6000 - 2000
x = $4000
