# Math Help - Investing money at different rates.

1. ## Investing money at different rates.

Okay

Sam has $12,000. He invests this money into a savings account and a bond account. The savings account has an interest rate of 4%, while the bond has a rate of 6%. The total interest he collected at the end of the year was$640. how much did he invest into each account? I've done these multiple times in class but I can't get the formula drilled into my brain.

i know that
x+y = 12000
and .04x + .06y = 640

x = savings
y = bond

so y = 12000 - x

.04x + .06(12000 - x) = 640
if i distribute i get..
.04x + 720 - .06x = 640
.04x -.06x = -.02x

-.02x + 720 = 640

this is where I got lost

this is where I got lost.

2. Originally Posted by qleeq
Okay

i know that
x+y = 12000
and .04x + .06y = 640

x = savings
y = bond
I would write it as

$x+y = 12000$
and $1.04x + 1.06y = 12000+640$

Now $y = 12000-x$

so

$1.04x + 1.06(12000-x) = 12000+640$

now solve for x and in turn find y

3. Originally Posted by pickslides
I would write it as

$x+y = 12000$
and $1.04x + 1.06y = 12000+640$

Now $y = 12000-x$

so

$1.04x + 1.06(12000-x) = 12000+640$

now solve for x and in turn find y
why did you change it to 104% when 640 was left the same in the original equation?

$1.04x + 12720 - 1.06x = 12640$
then
$-.02x + 12720 = 12640$
$-.02x = -80$
$-.02x/-.02 = -80/-.02$
$x = 4000$
$12000 - 4000 = 8000$
$x = 4000, y = 8000$

oh.. thanks lol

4. Originally Posted by qleeq
why did you change it to 104% when 640 was left the same in the original equation?
I don't understand this comment. I changed the 640 to 12000+640, the invested amount plus the interest.

5. Originally Posted by pickslides
I don't understand this comment. I changed the 640 to 12000+640, the invested amount plus the interest.
Well.. it was originally 4% and 6% which are .04 and .06 respectively.
so how did you get 1.04 and 1.06? just some elaboration on that is that i'm looking for.

6. 1.04 is the mulitplier for a 4% increase on the original investment.

1.06 is the mulitplier for a 6% increase on the original investment.