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Fatimah won RM20000 in a competition
Fatimah won RM20000 in a competition. She put all the money in a fixed deposit, trust fund and Tabung Haji. The amount she put in Tabung Haji is RM5000 more than that in trust fund. After one year, she received profit totaling RM850 from the three investments. The fixed deposit paid 3.5% annually, the trust fund paid 4.5% annually and Tabung Haji paid 4.5 % annually. (a) By denoting x, y and z as the amunt of money invested in fixed deposit, trust fund and Tabung Haji respectively, form a system of linear equatons based on the above information (b) Write the system of linear equations in the form of matrix equation. (c) Find the amount of money invested in each category of fund.
Expert Solution
a)
| Let the maount invested in fixed deposit be x, trust fund be y, Tabung Haji be z. |
| x+y+z = 20000 |
| z=y+5000 |
| 0.035x+0.045y+0.045z= 850 |
b)
First one is the coefficient matrix, second is the variable matrix.
c) Solution - by substituting equation 2 in 1,
x+ y+y+5000=20000
x+2y = 15000
x= 15000 - 2y
Substituting the value of x=15000-2y and z= y+5000 in equation 3,
7(15000-2y) +9y+ 9(y+5000) = 170000
On solving this ,
105000-14y+9y+9y+45000 =170000
150000+4y=170000
4y=170000-150000=20000
y=20000/4 = 5000
x = 15000-2y = 5000
z= y+5000 = 10000
So, The amounts invested in fixed deposit is 5000, trust fund is 5000 and Tabung Haji is 10000
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