Answer: she invested $2000 at 15% and $3000 at 16%
Step-by-step explanation:
Let x represent the amount which he invested in the account earning 15% interest.
Let y represent the amount which he invested in the account earning 16% interest.
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
Considering the account earning 15% interest,
P = $x
T = 1 year
R = 15℅
I = (x × 15 × 1)/100 = 0.15x
Considering the account earning 16% interest,
P = $y
T = 1 year
R = 16℅
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
0.31x = 620
x = 620/0.31 = 2000
y = x + 1000 = 2000 + 1000
y = 3000
