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%?

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Answer 1 · 2016-11-13T18:21:09

#$770#

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!