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 5100×x

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

8100×(4000−x)

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

5100×x+8100×(4000−x)=284

⇒5x100+32000−8x100=284

⇒5x+32000−8x=284×100

⇒−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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