A sum of 2300 is invested part of it at 4 interest and remai

A sum of $2300 is invested, part of it at 4% interest and remainder at 6%. If the interest earned by the 6% investment is $50 more than the interest earned by the 4% investment, find the amount invested at each rate.

Solution

Total amount = $2300

Let $x invested at 4% and remain amount would be (2300-x) would be invested at 6%.

Total Amount for $x at 4% would be = x+ 4% of x = x+ 0.4x = 1.4x

Total Amount for $(2300-x) at 6% would be = 2300-x + 6% of (2300-x) = 2300-x +0.6*2300 -0.6x

                                                               = 2300 -1.6x +1380 = 3680 -1.6x

We are given \" interest earned by the 6% investment is $50 more than the interest earned by the 4% investment\".

Therefore, 3680 - 1.6x is $50 more than 1.4x.

So, we can setup an equation,

3680 -1.6x = 1.4x +50

3630 = 3x

x= 3630/3 = 1210.

2300-x = 2300-1210 = 1090

Therefore, amount invested at 4% is $1200 and amount inverst at 6% is $1090.