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Question 1205323: Siti has RM450000 in her ASB. She wants to invest in Gading Mutual deposit, Maju
Makmur bar gold, Indah certificate deposit and Selamat Maju bar gold which pay
simple annual interest of 9%, 6%, 10% and 15%, respectively. Moreover, she wants
to combine annual return of 8% and want to have only one-third of investment in
Indah certificate deposit and Selamat Maju bar gold.
a. Write the linear model system equation for the whole investment.
c. Use elimination method to find each of the investment
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! ## Setting up the Linear Model
**Let's denote:**
* **G:** Amount invested in Gading Mutual Deposit
* **M:** Amount invested in Maju Makmur Bar Gold
* **I:** Amount invested in Indah Certificate Deposit
* **S:** Amount invested in Selamat Maju Bar Gold
**Based on the given information, we can set up the following system of linear equations:**
1. **Total Investment:** G + M + I + S = 450000
2. **Total Annual Return:** 0.09G + 0.06M + 0.10I + 0.15S = 0.08 * 450000
3. **Indah and Selamat Maju Investment:** I + S = (1/3) * 450000
## Solving the System Using Elimination Method
**Step 1: Simplify the Equations**
* Equation 2: 9G + 6M + 10I + 15S = 360000
* Equation 3: I + S = 150000
**Step 2: Eliminate a Variable**
* Let's eliminate S. From Equation 3, we can express S as:
* S = 150000 - I
* Substitute S in Equations 1 and 2:
* Equation 1: G + M + I + (150000 - I) = 450000
=> G + M + 150000 = 450000
* Equation 2: 9G + 6M + 10I + 15(150000 - I) = 360000
=> 9G + 6M - 5I = -750000
**Step 3: Simplify the Equations Further**
* Equation 1: G + M = 300000
* Equation 2: 9G + 6M - 5I = -750000
**Step 4: Eliminate Another Variable**
* Let's eliminate M. Multiply Equation 1 by -6 and add it to Equation 2:
* -6G - 6M = -1800000
* 9G + 6M - 5I = -750000
* -------------------------
* 3G - 5I = -2550000
**Step 5: Solve for G and I**
* From Equation 1, we can express M as:
* M = 300000 - G
* Substitute M in the simplified Equation 2:
* 3G - 5I = -2550000
* 3G - 5(150000 - G) = -2550000
* 8G = 1200000
* G = 150000
* Substitute G in M = 300000 - G:
* M = 300000 - 150000 = 150000
* Substitute G in I + S = 150000:
* I + S = 150000
* I + (150000 - I) = 150000
* S = 0
Therefore, the investments are:
* Gading Mutual Deposit: RM150,000
* Maju Makmur Bar Gold: RM150,000
* Indah Certificate Deposit: RM150,000
* Selamat Maju Bar Gold: RM0
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