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%?

1 Answer
Nov 13, 2016

$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!