Answer: 4500
Explanation:
Let's denote the amount the student invests at the 6% rate as x, and the amount he invests at the 9% rate as y.
We are given the following information:
Amount invested at 6%: x
Amount invested at 9%: y
Total inheritance: $12,000
Tuition cost: $945
The interest earned from the 6% investment can be calculated as 6% of x, which is 0.06x.
The interest earned from the 9% investment can be calculated as 9% of y, which is 0.09y.
Since the combined interest earned from both investments must cover the tuition cost of $945, we can write the following equation:
0.06x + 0.09y = 945
We also know that the total amount invested must be equal to the inheritance amount:
x + y = 12,000
We now have a system of two equations:
0.06x + 0.09y = 945
x + y = 12,000
We can solve this system of equations to find the values of x and y.
One way to solve this system is to multiply the second equation by -0.06 and add it to the first equation, eliminating the x variable:
-0.06(x + y) + 0.06x + 0.09y = -0.06(12,000) + 945
0.03y = -720 + 945
0.03y = 225
y = 225 / 0.03
y = 7500
Substituting the value of y back into the second equation, we can solve for x:
x + 7500 = 12,000
x = 12,000 - 7500
x = 4500
Therefore, the student should invest $4,500 at the 6% rate and $7,500 at the 9% rate in order to cover the tuition cost of $945 using the interest earned from the investments.