Question

A sum of $3500 is invested in two parts. One part brings a return of 5% interest and the other a return of 8% interest. The total annual interest earned is $250. Find the amount invested at the 8% rate.

Answer 1

Let x represent the amount invested that brings 5% of interest.

Let y represent the amount invested that brings 8% of interest.

Then you can say that

$x+y=3500$

Next, the total annual interest is $250

5% of x can be expressed as: 0.05x

8% of y can be expressed as: 0.08y

Together both invesments bring:

$0.05x+0.08y=250$

With this we have established a system of two equations with two unknowns.

Next clear one of the expressions in terms of one of the unknowns:

$\begin{gathered} x+y=3500 \\ x=3500-y \end{gathered}$

Replace this in the second equation and solve:

$\begin{gathered} 0.05x+0.08y=250 \\ 0.05(3500-y)+0.08y=250 \\ 0.05\cdot3500-0.05y+0.08y=250 \\ 175+0.03y=250 \\ 0.03y=75 \\ y=2500 \end{gathered}$

The amount invested at the 8% rate is $2500