Answer:
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
