Zoe has a total of $4,000 invested in two accounts. One account pays 5% interest, and the other pays 8% interest. How much does she have invested in each account if her total interest for a year is $284?

A. $1,200 at 5% & $2,800 at 8%
B. $1,600 at 5% & $2,400 at 8%
C. $2,400 at 5% & $1,600 at 8%
D. $2,800 at 5% & $1,200 at 8%

1 Answer
Pallu
Feb 4, 2018

A. $1,200 at 5% & $2,800 at 8%

Explanation:

Zoe has a total of $4,000 invested in two accounts.

Let the investment in first account be #x#, then

The investment in second account will be #4000 - x#.

Let the first account be the one account paying 5% interest, So:

The interest will be given as #5/100 xx x#

and the other paying 8% interest can be represent ed as:

#8/100 xx (4000-x)#

Given that: her total interest for a year is $284, that means:

#5/100 xx x + 8/100 xx (4000-x)= 284#

#=> (5x)/100 +(32000 -8x)/100 = 284#

#=> 5x + 32000 - 8x = 284 xx 100#

#=> -8x+5x = 28400 - 32000 #

# => -3x = - 3600#

#=> x= $1200# ------ amount invested in first account with 5% interest.
#=> 4000 -1200 = $2800 # ------- amount invested in second account with 8% interest.

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