Phyllis invested 31000 dollars a portion earning a simple in

Phyllis invested 31000 dollars, a portion earning a simple interest rate of 4 percent per year and the rest earning a rate of 6 percent per year. After one year the total interest earned on these investments was 1620 dollars. How much money did she invest at each rate?

Solution

Let x= the amount invested at a rate of 4% per year and

y= the amount invested at a rate of 6% per year.

Then x + y = 31000 ... (1)

Total interest = 1620

x(0.04)(1) + y (0.06)1 = 1620

0.04x + 0.06 y = 1620

Multiply both sides by 100,

4x + 6y = 162000

Divide both sides by 2,

2x + 3y = 81000 ...(2)

Now (2) + -2* (1),

2x + 3y = 81000

-2x - 2y = -62000

Adding,

y = $ 19000

Substitutiong this in (1),

x + 19000 = 31000

x = 31000 - 19000= $12000

So the amount invested at 4% rate = $12000 and

the amount invested at 6% rate = $19000