Question

6,000 dollars is invested in two different accounts earning 3% and 5% interest. At the end of one year, the two accounts earned $220 in interest. How much money was invested at 5%? $2,000 $3,000 $4,000

Answer 1

$2000

Explanation:

6,000 dollars is invested in two different accounts earning 3% and 5% interest.

Let x be the amount invested in account earning 3% interest

So, 6000-x is the amount invested in account earning 5% interest

`S.I. =(P* R* T)/(100)`

So, Simple interest for account earning 3% interest

`S.I. =(x * 3 * 1)/(100)`

`S.I. =0.03x`

Simple interest for account earning 5% interest

`S.I. =((6000-x) * 5 * 1)/(100)`

`S.I. =0.05(6000-x)`

`S.I. =300-0.05x`

Since we are given that the two accounts earned $220 in interest

So,
`0.03x+300-0.05x=220`

`−0.02x+300=220`

`80=0.02x`

`(80)/(0.02)=x`

`4000=x`

So, 4000 was invested at 3%

(6000-x)=6000-4000=2000 was invested at 5%

Hence 2000 was invested at 5%