Question

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%

Answer 1

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.