Question

Question #426f6

Answer 1

We're going to use "`x`" as our variable for the part of the $25,000 that is invested at `5%`.

(We could have chosen the `6%` - it doesn't matter.)

Explanation:

First, draw a circle, or just a blob shape, and draw a sort-of wavy line thru it.

The whole circle is the $25,000.

Label one side of the circle "`x`", and the other side "`25,000 - x`".
(It doesn't matter which side you choose for `x`.)

In the part of the circle that's `x`, write `5%` - the interest rate for that portion of the $25,000.

In the other part of the blob, write `6%` - the interest rate for the portion of the money that's `25,000 - x`.

Now, we use the formula: `I = Prt`.

Interest equals the Principle (the starting amount of money) times the (interest) rate times the time period of the investment.

The time period is one year, so we're not going to write a `1` in there.

We have: `I = P*r`.

The Interest = `$1350`, so we're going to set up the equation like this:

`1350 = [(25,000-x)*(.06) + (.05)x]`

The "interest" part of the equation inside the square brackets is in two parts because the principle amount is in two parts - one part invested at `5%` and the other part invested at `6%`.

Multiply inside the brackets:

`(25,000) * (.06) = 1500` and `.06 * x = .06x`

Inside the brackets we have `[1500- .06x+ .05x]`.

Simplify this:

`[1500 - .01x]`

Our equation is now:

`1350 = [1500 - .01x]`

Multiply both sides by `100` to remove the decimal fraction, and we get:

`135,000 = 150,000 - x`

Subtract the `150,000` to move it over:

`135,000 - 150,000 = - x`

`-15,000 = -x`

Multiply both sides by `(-1)`:

and `x = 15,000`.

If `x = $15,000`, then `$25,000 - x = $10,000`.

The `x` part was invested at `5%`:

`$15,000 * (.05) = $750`

and the `$10,000` invested at `.06 = $600`

`$750 + $600 = $1350`.

(You just checked the answer.)

`$15,000` was invested at `5%`, and `$10,000` was invested at `6%`.