I need help with my home work

Question

Country Day's scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. CDs pay 5.75 % interest, bonds pay 2.4 % interest, and stores pay 10.7 % interest. Country day invests $ 35000 more in bonds than in CDs. If the investment's annual income is $ 9960, how much was invested in each vehicle?

Maricopa Success invested $_______     in stocks.

Maricopa Success invested $________     in bonds.

Maricopa Success invested $__________     in CDs.

Answer 1

.107s +.024b +.0575c = 9,960

b = 35,000 + c

s+b+c = 145,000

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

s= 145,000 - b -c = 145,000-35,000-c -c = 110,000 -2c

.107(110,000-2c) +.024(35000+c) + .0575c = 9960

-.214c + .024c + .0575c = 9960 -.107(110,000) - .024(35,000)

(.0815-.214)c = 9960- .107(110,000)-.024(35,000)

c= (9,960-11,770 - 714)/(-.1325)

c= 2,524/.1325

c= about $19,049.06 invested in CD's

b = 35000+c =about $44,049.06 invested in bonds

s = 145,000 -b -c = 145000- 44,049.06- 19,049.06

s = $81,901.88 invested in stocks

a very rough check on the answers:

each = about s=82, b=44, c=19

10.4(82) +.024(44)+ .0575(19)

=8.5 + 1.06 + 1.09

=about 10.6 which is roughly close to 9.96

average rate of return = about 6.9% = 9960/145000