Sara invested $8,000, part at 6% and the rest at 9% interest per year. How much did she invest at each rate if her total return per year on the investment was $660?

Question

mathstudent55 · Answer

I = Prt
I = interest, P = principal, r = rate, t = time
Let's say she invested x at 6%.
That means she invested 8000 - x at 9%.
Can you write an expression for the interest earned at 6% and an expression for the interest earned at 9%?

anonymous · Answer

how?

anonymous · Answer

is it .06x+.09y=660?

mathstudent55 · Answer

I = Prt
I = I
P = x
r = 6%
t = 1
Use the equation above and the info above to write one expression for the interest earned at 6%

mathstudent55 · Answer

Yes, but you can do one thing now.

mathstudent55 · Answer

You used x for the amount invested at 6% and y for the amount invested at 9%.
What do we know about x and y?

anonymous · Answer

they're different variables?

mathstudent55 · Answer

Where does the 8000 come in?

anonymous · Answer

.06

anonymous · Answer

and .09?

anonymous · Answer

so i plug in 800 for  x and y?

mathstudent55 · Answer

No.
Your equation above is correct.
You used x as the part of the $8000 amount invested at 6%.
You used y as the part of the $8000 amount invested at 9%.
Using x, y, and 8000, can you write the relation between x and y?

mathstudent55 · Answer

The total amount invested is $8000.
x was invested at 6%. y was invested at 9%.
x + y = ?

anonymous · Answer

.06(800)+.09y=660?

anonymous · Answer

then y =6800

anonymous · Answer

but i don't understand what to do next?

mathstudent55 · Answer

No.
You need a second equation which is 
x + y = 8000

Now you have a system of equations:
0.06x + 0.09y = 660
x + y = 8000

anonymous · Answer

.06x+.09(6800)=660
x=-800?
is that right?

anonymous · Answer

so for the second eqatuion do i plug in x=-800 and y=6800?

anonymous · Answer

help?

anonymous · Answer

can you just give me the answer please?

mathstudent55 · Answer

Where do you get 800 from. It's 8000.
Ok, we have two equations,
0.06x + 0.09y = 660
x + y = 8000

Let's use the substitution method to solve the system of equations.

mathstudent55 · Answer

We solve x + y = 8000 for y:
y = 8000 - x

Now we replace y with 8000 - x in the first equation:
0.06x + 0.09(8000 - x) = 660
0.06x + 720 - 0.09x = 660
-0.03x = -60
x = 2000

x + y = 8000
2000 + y = 8000
y = 6000

Answer: $2000 invested at 6% and $6000 invested at 9%

anonymous · Answer

THANK YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!