Solving a tax rate or interest rate problem using a system of linear equations

Question

Last year, Brian had $30,000

 to invest. He invested some of it in an account that paid 7%

 simple interest per year, and he invested the rest in an account that paid 9%

 simple interest per year. After one year, he received a total of $2200

 in interest. How much did he invest in each account?

Answer 1

Here's another solution in case you are unfamiliar with or not comfortable with systems of equations.

7%x+9%(30,000-x)=2200 where x=amount invested at 7%

0.07x+0.09(30,000-x)=2200

0.07x+2700-0.09x=2200

-0.02x+2700=2200

-0.02x=-500

0.02x=500

2x=50000

x=25000, x=$25,000 invested at 7%

30,000-25,000=5000, $5,000 invested at 9%

Answer 2

Let x be the amount invested at 7% and y be the amount invested at 9%.

x + y = 30000 Eqn1

0.07x + 0.09y = 2200

Scaling by 100

7x + 9y = 220000 Eqn2

Multiplying Eqn1 by 9 and subtracting Eqn2

9x + 9y = 270000

7x + 9y = 220000

-----------------------

2x = 50000

x = 25000

y = 5000