Final answer:
The investment club placed $5,000 at 9% and $4,500 at 8%. This was determined by solving a system of linear equations representing the total interest earned from each account and with amounts reversed in each account.
Step-by-step explanation:
The question relates to solving a system of linear equations derived from the information about the investments made by an investment club in two different simple interest accounts.
Let's denote the amount invested at 9% as x and the amount invested at 8% as y.
The total interest earned for one year is $810, which gives us the first equation:
0.09x + 0.08y = 810
If the amounts placed in each account had been reversed, the interest earned would have been $805. This gives us the second equation:
0.08x + 0.09y = 805
Solving these two equations simultaneously will give the amounts placed in each account at 9% and 8% respectively.
Let's multiply the first equation by 9 and the second equation by 8 to eliminate the decimals and simplify:
0.81x + 0.72y = 7290
0.64x + 0.72y = 6440
Subtracting the second equation from the first yields:
0.17x = 850
Divide both sides by 0.17 to find x:
x = 5000
Substitute x back into one of the original equations to solve for y:
0.09(5000) + 0.08y = 810
450 + 0.08y = 810
0.08y = 810 - 450
0.08y = 360
Divide both sides by 0.08 to find y:
y = 4500
Therefore, the investment club placed $5,000 at 9% and $4,500 at 8%.