Matrix inverse and matrix equations

Question

Maricopa’s success scholarships fund receives a gift of $155,000. The money is invested in stocks , bonds and CD’s , CD’s pay 2.25% of interest. Bonds pay 4.5% of interest. And stocks pay 6.4% in interest. Maricopa’s success invests $40,000 more bonds the. CD’s . If the annual income from the investment is $6740 , how much was invested in each account?

Answer 1

X is amount in stocks

Y is the amount in bonds

Z is the amount in CDs

X+ Y + Z = 155000

Y = Z + 40000

0.064X + 0.045y + 0.0225Z = 6740

Substitutes Y=z+40000 into the first and third equations.

You get;

X + 2z = 115000

0.064X + 0.0675z = 4940

solving the first equation for x and clearing the decimals from the second

x = 115000 - 2z

640 x + 675z = 49400000

Substitution gives your z = 40000

Then x = 35000 which forces y=80000