Extremely Stuck

Question

Maricopa's Success scholarship fund receives a gift of $ 140000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 3 % interest, and stocks pay 8.9 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 8057.5 , how much was invested in each account?

Answer 1

Let "s" represent the amount invested in stocks. Let "b" be the amount invested in bonds. And let "c" be the amount invested in CDs.

Since it says the money is invested, we can assume ALL the money is invested so:

(1) s + b + c = 140000

We are told that $15000 more was invested in bonds than in CDs so (since bonds is more than CDs):

(2) b = c + 15000

Since the annual income is $8057.50, then:

(3) 0.089s + 0.03b + 0.0475c = 8057.5

So we have 3 equations in 3 unknowns and can solve them. You can choose a matrix method, you can use elimination, or you can use substitution. Substitution is fairly straight forward. Equation (2) says "b" is the same thing as "c + 15000" so plug "c + 15000" in for "b" in equation (1):

s + (c + 15000) + c = 140000

s + 2c + 15000 = 140000

s = 125000 - 2c

Now, using equation (3) plug in "c + 15000" in for "b" and "125000 - 2c" in for "s" to get:

0.089(125000 - 2c) + 0.03(c + 15000) + 0.0475c = 8057.5

11125 - 0.178c + 0.03c + 450 + 0.0475c = 8057.5

-0.1005c + 11575 = 8057.5

-0.1005c = -3517.5

c = 35000

Then, plugging c = 35000 into s = 125000 - 2c we get s = 125000 - 2(35000) = 55000

And plugging c = 35000 into b = c + 15000 we get b = 35000 + 15000 = 50000

So $55,000 was invested in stocks, $50,000 was invested in bonds and $35,000 was invested in CDs