# 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%

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 $\frac{5}{100} \times x$and the other paying 8% interest can be represent ed as: $\frac{8}{100} \times \left(4000 - x\right)$Given that: her total interest for a year is$284, that means:

$\frac{5}{100} \times x + \frac{8}{100} \times \left(4000 - x\right) = 284$

$\implies \frac{5 x}{100} + \frac{32000 - 8 x}{100} = 284$

$\implies 5 x + 32000 - 8 x = 284 \times 100$

$\implies - 8 x + 5 x = 28400 - 32000$

$\implies - 3 x = - 3600$

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