Question

Solve this problem by using a two order system. A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate? $ a0 at 4% and $ a1 at 3%

Answer 1

Let $x be the amount of money that a man invested in 3% account and $y be the amount of money a man invested at 4% account. The problem can be modelled by the system of two equations.

1. The income for the 1st investment is $0.03x and the income for the 2nd investment is $0.04y.

If his total income for the two investments is $194, then

0.03x+0.04y=194.

2. If a man invests $5,200, part at 4% and the balance at 3%, then

x+y=5,200.

3. You get a system of equations:

$\left\{\begin{array}{l}x+y=5,200\\0.03x+0.04y=194\end{array}\right.$

From the 1st equation express x and substitute it into the 2nd equation:

$0.03(5,200-y)+0.04y=194,\\ \\156-0.03y+0.04y=194,\\ \\0.01y=38,\\ \\y=\ 3,800.$

Then

$x=\ 5,200-\ 3,800=\ 1,400.$

Answer: $1,400 at 3% and $3,800 at 4%.