Amanda invested a total of $3 comma 100 into three separate accounts that pay 4 % , 6 % and 7 % annual interest. Amanda has three times as much invested in the account that pays 7 % as she does in the account that pays 4 %. If the total interest for the year is $ 191 comma how much did Amanda invest at each rate?

the amount invested at 4% interest is $5,00

the amount invested at 6% interest is $1,100

the amount invested at 7% interest is $1,500

Explanation:

Data provided in the question:

Total amount invested = $3,100

Interest rates : 4% , 6 % and 7 %

Total interest = $191

Now,

Let the amount invested at 4% interest be 'x'

the amount invested at 6% interest be 'y'

the amount invested at 7% interest be 'z'

Therefore,

According to the question:

x + y + z = $3,100 ... (1)

z = 3x ... (2)

0.04x + 0.06y + 0.07z = $191 ... (3)

From (1) and (2), we have

x + y + 3x = $3,100

or

4x + y = $3,100

or

y = $3,100 - 4x, ... (4)

from 2, 3 and 4, we have

0.04x + 0.06 ($3,100 - 4x) + 0.07 (3x) = $191

⇒ 0.04x + 186 - 0.24x + 0.21x = $191

⇒ 0.01x + 186 = $191

⇒ 0.01x = 5

or

x = $500

thus,

from (2)

z = 3 * 500

or

z = $1,500

From (4)

y = $3,100 - 4 (500)

or

y = $1,100

Hence,

Amanda invested

the amount invested at 4% interest is $5,00

the amount invested at 6% interest is $1,100

the amount invested at 7% interest is $1,500