Question

A total of $12,000 is invested in two funds paying 9% and 11% simple interest. If the yearly interest is $1,180, how much of the $12,000 is invested at each rate?
We have two unknowns: the amount of money invested at 9% and the amount of money invested at 11%.

Sentence (1) ''A total of $12,000 is invested in two funds paying 9% and 11% simple interest.'' can be restated as (The amount of money invested at 9%) (The amount of money invested at 11%) $12,000.

Sentence (2) ''If the yearly interest is $1,180, how much of the $12,000 is invested at each rate?'' can be restated as (The amount of money invested at 9%) 9% + (The amount of money invested at 11% 11%) total interest of $1,180.
In shortcut form: (1) x+y=$12000 (2) .09x+.11y=$1180

Principal of P dollars = P dollars* Rate in decimal * time in years
Can you show me how you get interest 0.09x on aPrincipal of x dollars?

Answer 1

from your first equation
x + y = 12000 ---> y = 12000 - x

sub that into the other equation:
.09x + .11y = 1180
.09x+ .11(12000-x) = 1180
.09x+ 1320 - .11x = 1180
-.02x = -140
x = 7000
then y = 12000 - 7000 = 5000

$7000 was invested at 9%, and $5000 was invested at 11%

check:
.09(7000) + .11(5000)
= 630 + 550 = 1180

Answer 2

Suppose that $2000 is invested at a rate of 3.3% ,total amount after 3 years.