Green River Community College's scholarship fund receives a gift of $ 160000. The money is invested in stocks, bonds, and CDs. CDs pay 2 % interest, bonds pay 2.8 % interest, and stocks pay 9.8 % interest. GRCC invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 7580, how much was invested in each vehicle?

amount invested in Stocks = $50,000

amount invested in bonds = $60,000

amount invested in CDs = $50,000

Explanation:

Let amount invested in Stocks be 's'

amount invested in bonds be 'b'

amount invested in CDs be 'c'

Now,

According to the question

s + b + c = $160,000 ... (1)

b = c + 10,000 ... (2)

and,

0.098s + 0.028b + 0.02c = $7580 ... (3)

substituting b from 2 in equation 1

we get

s + c + 10,000 + c = $160,000

or

s + 2c = 150,000

or

s = 150,000 - 2c ... (4)

substituting s from 4 and b from 2 in 3, we get

0.098 (150,000 - 2c) + 0.028 (c + 10,000) + 0.02c = $7580

or

14700 - 0.196c + 0.028c + 280 + 0.02c = 7580

or

-0.148c = - 7400

or

c = $50,000

Therefore,

s = 150,000 - 2 (50,000)

or

s = 50,000

and,

b = (50,000) + 10,000

= 60,000

Hence,

amount invested in Stocks = $50,000

amount invested in bonds = $60,000

amount invested in CDs = $50,000