Question

You are going to invest $25, 000, part at 14% and part at 16%. What is the most that can be invested at 14% in order to make at least $3, 600 interest per year?

Answer 1

If I'm not mistaken, you have to make two separte equations:
\[\LARGE x+y=25000\]
\[\LARGE 0.14x+0.16y=3600\]

Answer 2

hmm.. i dont get it..

Answer 3

Okay, so we are investing $25,000 right? Well we have to separate them evenly into two different accounts so we can earn an additional $3,600.
The x+y just says that this much money plus this other half add up to the total $25,000.

Answer 4

With those given equations we can find out how much x and y are.

Answer 5

uh..

Answer 6

Has your teacher taught you this yet? Or is completely new?

Answer 7

completely new.. he just gave us activities

Answer 8

Are you completely lost on what I'm saying? Or do you at least have an idea on what I'm saying.

Answer 9

lost sir. im sorry.

Answer 10

You are going to invest $25, 000, part at 14% and part at 16%. What is the most that can be invested at 14% in order to make at least $3, 600 interest per year?

Ok we have two different "values" essentially that we are going to invest.

x at 14%
y at 16%

Your total investment will be the sum of those two values. And your total investment is 25,000

\(x+y=25,000\)

Make sense?

Now, the interest rates are different for x and y. We want the interest rates of each of them added to be 3,600.

\(0.14x+0.16y=3,600\)

Now we have a system of equations that can be solved.

\(x+y=25,000\)
\(0.14x+0.16y=3,600\)

Have you covered how to solve these?

Answer 11

0.14x+0.16y=3600?

Answer 12

I'm not sure what you are asking.

Answer 13

That is just for the interest, remember the 14% and 16% interest?

Answer 14

0.14x+0.16y=3600? im dont know what to do next..

Answer 15

No, with these problems, you have to look at both equations.

\(x+y=25,000\\
0.14x+0.16y=3,600\)

What we can do is solve for y in the first equation, and plug it into the second equation.

\(y=25,000-x\)

\(0.14x+0.16(25,000-x)=3,600\)

Then we can solve for x.
Do you think you could solve it from there?

Answer 16

Austin might take the spotlight now xD

Answer 17

@MysteryOwl For now, just worry about solving the equation.

Answer 18

let me try it :)

Answer 19

is this correct?

0.14x + o.16 (25000-x)=3600
0.14x + 4000-0.16x=3600
-0.02x =3600-4000
-0.02x=-400
-0.02x/-0.02=-400/-0.02
x=200000

Answer 20

Is that 20,000 or 200,000?

Answer 21

200,000

Answer 22

That's strange..

Answer 23

why?

Answer 24

How is it possible to put in $200,000 when you only have 20,000?

Answer 25

:O something must be wrong in my solution.

Answer 26

But anyways, forget that one, try solving for y, that one will make sense.

Answer 27

I promise you, if we solve for y it will make so much more sense. :)

Answer 28

okies xD let me try again :)

Answer 29

y=5000

Answer 30

Now that makes sense.
So now that we have y, we can plug that back into the equation to solve for x. So now solve:
x+5000=25000

Answer 31

x=2000

Answer 32

So 2,000+5,000=25,000?

Answer 33

no xD its 20000

Answer 34

There you go :)
And that's pretty much it for solving.

Answer 35

so the answer are x=20000 and y=5000.. are there no other solutions to make?

Answer 36

You could of also checked your answers by graphing the systems:

Answer 37

And nope, that's it.

Answer 38

that was an awesome :) thanks..

Answer 39

And sorry about the confusion earlier, as you go further into the chapter you will understand it more.