Help me please as I get confused and get negative numbers.

Question

Maricopa's Success scholarship fund receives a gift of $ 140000. The money is invested in stocks, bonds, and CDs. CDs pay 5.25 % interest, bonds pay 3.6 % interest, and stocks pay 6.7 % interest. Maricopa Success invests $ 30000 more in bonds than in CDs. If the annual income from the investments is $ 7085, how much was invested in each account?

Maricopa Success invested   in stocks.

Maricopa Success invested   in bonds.

Maricopa Success invested    in CDs.

Answer 1

.036b + .0525c + .076s = 7085= interest on 3.6% from bonds, 5.2% from cds and 7.6% from stocks

b+c+s = 140,000 = total invested in bonds, cds and stocks

b= 30,000+ c ($30,000 more invested in bonds than in cds)

3 equations, 3 unknowns, solve by substitution, elimination or matrix algebra

s = 140000-30,000 -c -c = 110,000 -2c

.036(30,000 +c) +.0525c + .076(110,000-2c) = 7085

.036c +.0525c -.076(2c) = 7085 -.036(30,000) -.076(110,000)

.0885c -.152c = 7085 -1080 - 8360

-.0635c = 7085-9440= - 2355

c = -2355/-0635= $37,086.61 invested in cds

b = $40,086.61 invested in bonds

s = 110,000-2(37,086.61) = $35,826.77 invested in stocks

7085/140000= about 5.06%

3.6, 5.25 and 7.6 average to about 5.48% not far from 5.06%

which suggests there may be "roughly" equal amounts invested in bonds, cds & stocks

37,086, 40,087 and 35,827 are roughly equal

7.6- 5.48 = 2.12

5.48-5.25 = 0.23

5.48-3.6 = 1.88

3.6% is a little closer to the average rate of return 5.48%, than 7.6%, so you'd expect a little more invested at 3.6% than at 7.6%

37,086 is a little more than 35,827