**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.**

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