help with math

Question

Country Day's scholarship fund receives a gift of $ 150000. The money is invested in stocks, bonds, and CDs. CDs pay 3.25 % interest, bonds pay 4.4 % interest, and stocks pay 7.9 % interest. Country day invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 6900 , how much was invested in each vehicle?

Country Day invested $                 in stocks.

Country Day invested $                 in bonds.

Country Day invested $                  in CDs.

Answer 1

X is stocks

Y is bonds

Z is CDs

 

 X+Y+Z = 150000

 

 X + (Z+25000) + Z = 150000

 

 X + 2Z + 25000 = 150000   

 

 X + 2Z = 125000

 

 X = 125000 -2z

 

 

 

 0.079X + 0.044Y + 0.0325Z = 6900

 

0.079X + 0.044(Z+25000) + 0.0325Z = 6900

 

0.079X + 0.044Z + 1100 + 0.0325Z = 6900

 

0.079X +  0.0765Z + 1100 = 6900

 

0.079X + 0.0765Z = 5800

 

0.079(125000 - 2z) + 0.0765z = 5800

 

9875 - 0.158z + 0.0765z = 5800

 

-0.0815z = 5800-9875

 

z=50000

 

x=25000

 

y = 75000