Elimination problem

Question

Country Day's scholarship fund receives a gift of $ $143,680.43. The money is invested in stocks, bonds, and CDs. CDs pay 2.75 % interest, bonds pay 3.9 % interest, and stocks pay 11 % interest. Country day invests $ $72,025.80 more in bonds than in CDs. If the annual income from the investments is $ $8,986.84, how much was invested in each vehicle?

Answer 1

2.75% = .0275 and 3.9% = .039

X = amount invested in CDs
Y = amount invested in Bonds
Z = amount invested in stocks

X + Y + Z = 143680.43

Y = X + 72025.80

.0275X + .039Y + .11Z = 8986.84


Substituting the second equation into the third:

0.0275X + .039 (X + 72025.8) + .11Z = 8986.84

0.0275X + .039X + 2809 + .11Z = 8986.84

0.0665X + .11Z = 6177.84 <--- call this equation ALPHA


Substituting the second equation into the first equation:

X + (X + 72025.80) + Z = 143680.43
2X + 72025.8 + Z = 143680.43

2X + Z = 71654.63

solving for Z = 71654.63 - 2X

Substituting this into equation ALPHA above:

0.0665X + .11 ( 71654.63 - 2X) = 6177.84

0.0665X + 7882 - .22X = 6177.84

-.1535X = -1704.16

X = 11102.02

Then Y = X + 72025.8 = 11102.02 + 72025.8 = 83127.82

and Z = 71654.63 - 2X = 71654.63 - 2(11102.02) = 49450.59

CHECK:
11102.02 x .0275 + 83127.82 x .039 + 49450.59 x 0.11 = 8986.85

The discripency in the pennies digit is due to rounding.

The problem CLEARLY states that the funds are invested in all
3 vehicles and the numbers don't work out if no funds are invested
in stocks.