setting up story problems

Question

An accountant invests part of a $6000 bonus in a 5% simple interest account and invests the remainder of the money at 8.5% simple interest.  Together the investments earn $370 per year.  Find the amount invested at each rate.

Answer 1

Hi Greg,

 

So we know that we are investing a total of $6000, into two different accounts: one that earns 5% simple interest, and one that earns 8.5% simple interest. Let's say that:

 

    x = amount invested into the 5% account

 

    y = amount invested into the 8.5% account

 

We know that we are only investing a total of $6000, so we could also say that:

 

    x + y = 6000, or

 

    y = 6000 - x

 

The amount earned each year by the 5% account would be:

 

    x * .05

 

The amount earned each year by the 8.5% account would be:

 

    y * .085, or using the "y = 6000 - x" substitution we found above,

 

    (6000 - x) * .085

 

Finally, we know that the total earnings each year are $370:

 

    .05x + .085 (6000-x) = 370

 

Now we have an equation with just one variable "x", which we can solve for:

 

    .05x + 510 - .085x = 370

 

    -.035x + 510 = 370

 

    140 = .035x

 

    4000 = x

 

So, the accountant must have invested $4000 into the account with a 5% return, which means that:

 

    y = 6000 - x

 

    y = 6000 - 4000

 

    y = 2000

 

The accountant invested $2000 into the account with a 8.5% return. 

 

Now let's check the answer:

 

    $4000 (.05) + $2000 (.085) should equal $370

 

    $200 + $170 = $370

 

    $370 = $370, so our answer checks.

 

I hope this helps!

 

Andy