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Matrix Dalia inherited $15,000.00 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund. After 1 year, she recei

Dalia inherited $15,000.00 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund. After 1 year, she received a total of $730.00 in simple interest from the 3 investments.
 
The money market account paid 4% annually, the bonds paid 5% annually, and mutually funds paid 6% annually. There was $2,000.00 more invested in the mutual fund than in bonds. Find the amount that Dalia invested in each category using any matrix method you know.
 
 
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3 Answers

X - invested in mutual fund 
 X - 2000- invested in bonds
15000 - ( 2X - 2000) = 13,000 -2X - invested money market
 
  (13000 -2x ) 0.04 + ( X - 2000)0.05 + X(0.06) = 730
 
  520 - 0.08X + 0.05X  - 100 + X (0.06) = 730
 
   0.03 X = 210
 
   X = 7,000  / invested in mutual funds
 
 
   X - 2000 = 5000 / invested   in bonds
 
   3.000 = invested in money market.
   
 
Inherited: $15,000
 
Simple Interest Earned: $730.00
 
Money Market: 4%; Bonds: 5%; Mutual Funds: 6%
 
MONEY MARKET + BONDS + MUTUAL FUNDS = $15,000
 
0.04 MONEY MARKET + 0.05 BONDS + 0.06 (MUTUAL FUNDS= (BONDS + $2000)) = $730
 
BONDS + $2000 = MUTUAL FUNDS
 
From there, you can set up a matrix, or solve using a system of equations like the Gaussian-Jordan method.
Dalia inherited $15,000.00 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund. After 1 year, she received a total of $730.00 in simple interest from the 3 investments.

The money market account paid 4% annually, the bonds paid 5% annually, and mutually funds paid 6% annually. There was $2,000.00 more invested in the mutual fund than in bonds. Find the amount that Dalia invested in each category using any matrix method you know.

x = amount in money market
y = amount in municipal bonds
z = amount in mutual fund

x + y + z = 15000
4x + 5y + 6z = 73000
z = y + 2000 => 0x - y + z = 2000

Let’s create an Augmented Matrix and perform Row Operations on it to change it to a Reduced Row Echelon Form; from which we get the answers.

R1 1, 1, 1, 15000
R2 4, 5, 6, 73000
R3 0, -1, 1, 2000

R1 > R1 + R3
R2 > R2 - 4*R1

R1 1, 0, 2, 17000
R2 0, 5, -2, 5000
R3 0, -1, 1, 2000

R2 > R2 + 5*R3

R1 1, 0, 2, 17000
R2 0, 0, 3, 15000
R3 0, -1, 1, 2000

R2 > R2/3
R3 > -R3

R1 1, 0, 2, 17000
R2 0, 0, 1, 5000
R3 0, 1, -1, -2000

R1 > R1 - 2*R2
R3 > R3 + R2

R1 1, 0, 0, 7000
R2 0, 0, 1, 5000
R3 0, 1, 0, 3000

Swap R2 & R3 [optional]

R1 1, 0, 0, 7000
R2 0, 1, 0, 3000
R3 0, 0, 1, 5000

Solution: ($7000,$3000,$5000)

check:

(7000) + (3000) + (5000) =? 15000
15000 = 15000 √

4(7000) + 5(3000) + 6(5000) =? 73000
28000 + 15000 + 30000 = 73000 √

- (3000) + (5000) =? 2000
-3000 + 5000 = 2000 √