Question

Dana invested $10,000. Part of the money was invested at 10% and the remainder at 14%. The total yearly income from these investments was $1220. How much was invested at 14%?

Answer 1

`$770`

Explanation:

This was a fun one, thanks!

You will want to set up two equations for the scenarios and then isolate one of the terms to find the other. Good times!

Let `x` be the amount invested at 10%
Let `y` be the amount invested at 14%

We know that `x` and `y` amount to $10,000 and that the interest generated equals $1,220, ergo:

`.1x + .14y = 1220`
`x + y = 10000`

Let's multiply the second line by .1 so that we can eliminate the `x` and identify `y`:

`.1x + .14y = 1220`
`.1x + .1y = 1000`

Subtract the second line from the first which leaves you with:

`.04y = 220`

Multipliy both sides by 100 (to eliminate the decimals and solve for `y`):

`4y = 22000`
`y = 5500`

Sub your `y` value into the original statement to find `x`:

`x + 5500 = 10000`
`x = 4500`

Now double check your work by subbing these values in to the second statement:

`.1x + .14y = 1220`
`.1(4500) + .14(5500) = 1220`
`450 + 770 = 1220`

Voila!