Answer: the amount of money invested at the 5% rate is $15000
Explanation:
Let x represent the amount of money invested at the rate of 5%.
Let y represent the amount of money invested at the rate of 8%.
Mrs. Mary Moolah invested $20,000 in two different types of bonds. This means that
x + y = 20000
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time
Considering the investment at the rate of 5%,
P = x
R = 5
T = 1
I = (x × 5 × 1)/100 = 0.05x
Considering the investment at the rate of 8%,
P = y
R = 8
T = 1
I = (y × 8 × 1)/100 = 0.08y
If Mrs. Moolah's combined profit from both investments was $1,150, it means that
0.05x + 0.08y = 1150 - - - - - -1
Substituting x = 20000 - y into equation 1, it becomes
0.05(20000 - y) + 0.08y = 1150
1000 - 0.05y + 0.08y = 1150
- 0.05y + 0.08y = 1150 - 1000
0.03y = 150
y = 150/0.03 = 5000
Substituting y = 5000 into x = 20000 - y, it becomes
x = 20000 - 5000
x = 15000