Jaime T. answered • 07/23/21

Duke Alum Math Tutor

A simple interest rate formula is:

I = PRT

We can simply represent the two investments as:

I_{1 }= P_{1}(0.05)(1) → I_{1 }= 0.05P_{1}

I_{2 }= P_{2}(0.06)(1) → I_{2 }= 0.06P_{2}

We also know:

I_{1} + I_{2} = 270

If we add the first two equations from above, we get:

I_{1} + I_{2} = 0.05P_{1} + 0.06P_{2}

this becomes:

First equation: 270 = 0.05P_{1} + 0.06P_{2}

We also know:

Second equation: 5000 = P_{1} + P_{2}

Now that we have our two equations, we can solve for P1 and P2.

First step is to multiply our second equation by 0.05 so:

First: 270 = 0.05P_{1} + 0.06P_{2}

Second: 250 = 0.05P_{1} + 0.05P_{2}

We can then subtract the second equation from the first to eliminate P1:

20 = 0.01P_{2 }→ P_{2 } = 2000

Lastly, we can recall that originally 5000 = P_{1} + P_{2}

Solving for P_{1 }gives us P_{1 } = 3000.

Overall, we initially invested $3000 for our 5% interest and $2000 for our 6% interest.