Question

$5400 
is invested, part of it at 
11% 
and part of it at 
6%. 
For a certain year, the total yield is 
$ 474.00. 
 How much was invested at each rate?
@Directrix

Answer 1

So think of it as a system of equations

We know total there was 5400 invested into 2 different accounts 'x' and 'y'

so

\[\large x + y = 5400\]

Now we know that if 'x' has an 11% interest rate and 'y' has a 6% interest rate...and together those interests totaled 474..we have

\[\large .11x + .06y = 474\]

Now just solve that system

Answer 2

so I would 5400* .11 and 5400 * 0.6?

Answer 3

Not quite, do you know how to solve a system of equations?

Answer 4

yea...a little...That's what I am learning in school as we speak

Answer 5

which method would I use? sub or elimination?

Answer 6

Well I would just use substitution here..

In that first equation, solve for either 'x' or 'y' ... your choice

Answer 7

I suck at substitution

Answer 8

Alright, so

\[\large x + y = 5400\]

Do you see how I got this equation?

Answer 9

yes

Answer 10

so I plug in x and y as 5400

Answer 11

And to check, do you see where I got the second equation as well?

Answer 12

yea

Answer 13

Alright good,

back to the first equation

\[\large x + y = 5400\]

we cannot say that x and y are 5400....that wouldnt make sense...instead, we can solve or 1 of those variables...lets say 'x'

To solve this equation for 'x'...lets subtract 'y' from both sides of the equation

\[\large x = 5400 - y\]

make sense?

Answer 14

yea

Answer 15

With that, and the fact that we have a second equation

\[\large .11x + .06y = 474\]

Since, from the first equation,we now know what 'x' equals...we can "substitute" it into this equation for 'x'

So

if \[\large x = 5400 - y\]

then this second equation will now be

\[\large .11(5400 - y) + 0.6y = 474\]

see what happened there?

Answer 16

yea..u plugged it in

Answer 17

Right,

Now we just solve...that .11 outside the parenthesis will be distributed...multiplied into both terms inside the parenthesis...so

\[\large .11(5400 - y) + 0.6y = 474\]

will now become

\[\large 594 - .11y + 0.6y = 474\]

We can simplify that further, and solve for 'y'...can you do that?

Answer 18

no

Answer 19

make y by itself?

Answer 20

Well, yes we can start with that...we have 2 'y' terms...how could we get them by themselves on 1 side of the equation?

Answer 21

subtract 11y from both sides

Answer 22

Nope, alright so

\[\large 594 - .11y + 0.6y = 474\]

is what we have

Lets start by combining the 2 'y' terms...

what is -0.11y + 0.6y?

Answer 23

11.6

Answer 24

No, we have 2 decimals

\[\large -0.11y + 0.6y=?\]

Answer 25

0.71...my bad

Answer 26

Remember that the 0.11 is NEGATIVE so we are adding the 0.6 to a negative 0.11

Answer 27

-0.49

Answer 28

So close, but still not quite...

Answer 29

Try it the other way

what is 0.6 minus 0.11 ?

Answer 30

0.49