1. A professor has RM 15000 to invest for one year, some are 8% and the rest are at 7% annual interest. If she will earn RM 1100 from these investments, how much did she invest at each rate? (4 marks)
x+y = 15000
.08x + .07y = 1100
Now just solve for x at 8% and y at 7%
To solve this problem, we can set up a system of equations. Let's assume she invested x amount of money at 8% interest and y amount of money at 7% interest.
The first equation represents the total amount of money invested, which is RM 15000:
x + y = 15000
The second equation represents the total interest earned, which is RM 1100:
0.08x + 0.07y = 1100
Now we can solve the system of equations to find the values of x and y.
One approach is to use substitution. Solve the first equation for x in terms of y:
x = 15000 - y
Substitute this value of x into the second equation:
0.08(15000 - y) + 0.07y = 1100
Simplify the equation:
1200 - 0.08y + 0.07y = 1100
Combine like terms:
0.01y = 100
Divide both sides by 0.01:
y = 10000
Now substitute this value of y back into the first equation to find x:
x + 10000 = 15000
x = 5000
Therefore, the professor invested RM 5000 at 8% interest and RM 10000 at 7% interest.