Explanation:
Let X be the amount invested in CDs, Y be the amount invested in bonds, and Z be the amount invested in stocks.
We know from the problem that:
X + Y + Z = 135000 ---(1) (the total amount invested is $135000)
0.0375X + 0.035Y + 0.097Z = 6337.5 ---(2) (the total annual income from the investments is $6337.5)
Y = X + 60000 ---(3) (the amount invested in bonds is $60000 more than the amount invested in CDs)
We can use equation (3) to substitute for Y in equations (1) and (2), then solve for X and Z as follows:
X + (X + 60000) + Z = 135000
2X + Z = 75000
0.0375X + 0.035(X + 60000) + 0.097Z = 6337.5
0.0725X + 0.097Z = 8550
Using the system of equations 2X + Z = 75000 and 0.0725X + 0.097Z = 8550, we can solve for X and Z to get:
X = 22500
Z = 78000
Substituting back into equation (3), we get:
Y = X + 60000 = 82500
Therefore, the amounts invested in CDs, bonds, and stocks were $22500, $82500, and $78000 respectively.