Answer:
Explanation:
Let's begin by assigning variables to represent the amounts invested in each vehicle.
Let x be the amount invested in CDs,
y be the amount invested in bonds, and
z be the amount invested in stocks.
From the problem statement, we know that:
x + y + z = 125000 (the total amount invested)
y = x + 60000 (the amount invested in bonds is $60000 more than in CDs)
0.0475x + 0.037y + 0.109z = 7970 (the total annual income from the investments)
We can use the second equation to substitute for y in the other two equations, giving us a system of two equations in two variables:
x + (x + 60000) + z = 125000
0.0475x + 0.037(x + 60000) + 0.109z = 7970
Simplifying the first equation, we get:
2x + 60000 + z = 125000
2x + z = 65000
Substituting z = 65000 - 2x into the second equation, we get:
0.0475x + 0.037(x + 60000) + 0.109(65000 - 2x) = 7970
Simplifying and solving for x, we get:
0.0475x + 0.037x + 0.109(65000) - 0.218x + 0.109(2x) = 7970 - 0.109(60000)
0.026x = 1730
x = 66538.46
So, $66538.46 was invested in CDs. Using the equations y = x + 60000 and z = 65000 - 2x, we can calculate that $126,538.46 was invested in bonds and $45,923.08 was invested in stocks.
Therefore, $66538.46 was invested in CDs, $126,538.46 was invested in bonds, and $45,923.08 was invested in stocks.