Answer: she invested $2000 at 15% and $3000 at 16%
Step-by-step explanation:
Let x represent the amount invested at 15%.
Let y represent the amount invested at 16%.
She invested part at 15% and 1000 more than this amount at 16%. This means that
y = x + 1000
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount invested.
P represents the principal or amount invested.
R represents interest rate
T represents the duration of the investment.
Considering the amount invested at 15%,
P = x
R = 15
T = 1
I = (x × 15 × 1)/100 = $0.15x
Considering the amount invested at 16%,
P = y
R = 16
T = 1
I = (y × 16 × 1)/100 = $0.16y
If she will earn $780 in interest in a year, it means that
0.15x + 0.16y = 780- - - - - - - - - - - - 1
Substituting y = x + 1000 into equation 1, it becomes
0.15x + 0.16(x + 1000) = 780
0.15x + 0.16x + 160 = 780
0.31x = 780 - 160 = 620
x = 620/0.31
x = 2000
y = x + 1000 = 2000 + 1000
y = 3000
