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Investment Word Problem

Q: Hakim invested $15000. He put part of it in a term deposit that paid 4% per annum, and the remainder in a treasury bill that paid 5% per annum. After one year, the total interest was $690. How much did Hakim invest at each rate?

A: You have two unknowns (the amounts invested at each rate), so you need two equations.

Step 1: State your unknowns:

x = amount of $ invested at 4%
y = amount of $ invested at 5%

Step 2: Set up your equations:

Eqn. 1: x+y=15000
Eqn. 2: 0.04*x + 0.05*y = 690

Step 3: Isolate for y in Eqn. 1:

y = 15000-x

Step 4: Plug this value for y into Eqn. 2, and then collect terms to isolate for x:

0.04*x + 0.05*y = 690
0.04*x +0.05(15000-x) = 690
0.04*x +0.05*15000 – 0.05*x = 690
750 – 0.01x = 690
750-690 – 0.01x = 690 – 690
750-690 – 0.01x = 0
60 = 0.01x
x = 6000

Step 5: Now substitute this back into Eqn. 1 to find y:

y = 15000 – x
y = 15000 – 6000
y = 9000

So the two amounts invested are $6000 and $9000.