Question

You invested a total of $6,000 in two funds earning 7% and 9$ simple interest. During 1 year, the two funds earned a total of $500 in interest. How much did you invest in each fund?

Answer 1

Not quite sure what I would do first

Answer 2

Need to set up 2 equations and then use elimination or substitution

Answer 3

Any certain formulas?

Answer 4

No..what would be your first equation using A for one fund and b for the other fund?

Answer 5

Well we know it has to equal 6,000

Answer 6

Good so A + B = 6000 would be your first equation how about the second equation?

Answer 7

Hint: let A represent the 7% fund and B represent the 9% fund...

Answer 8

Ok so the first equation would be .07+.09=6,000

Answer 9

Right?

Answer 10

No

Answer 11

A + B =6000 that is the first equation

Answer 12

Oh ok

Answer 13

So then would be be

Answer 14

Wait no nvm what I was about to do was wrong

Answer 15

OK

Answer 16

But to start its .07+.09= something right?

Answer 17

Very Good...So .07 of what and .09 of what???

Answer 18

Not quite sure

Answer 19

(Sorry math isn't my strongest subject)

Answer 20

OK how do you determine 3% interest of say 1000 dollars?

Answer 21

Multiply?

Answer 22

Yes .03 times 1000 = 30 which would be the amount of interest earned. So looking at the question .07(something) + .09 (something) = Interest Earned...Can you see? Now what would be the somethings we need to fill in?

Answer 23

So lets say something is A right?

Answer 24

So now it has to be what does it equal

Answer 25

One something is A and the other something would be B..because that represents the two funds...so you have .07(A) +.09(B) = What?

Answer 26

6,000?

Answer 27

No A + B =6000 which is the principal amount you started with... .07(A) + .09(B) is the interest earned....how much total interest did you earn?

Answer 28

Oooooooh 500

Answer 29

So now you have 2 equations which look like what?

Answer 30

A way to get the answer?

Answer 31

Yes show me the two equations

Answer 32

Ok so the first one is

Answer 33

A+B=6,000

Answer 34

2nd one is

Answer 35

.07A+.09B=500

Answer 36

Great..do you know how to solve by substitution?

Answer 37

Ummm

Answer 38

I don't get what you mean?

Answer 39

what we are going to try to do is create an equation with only one variable (either A or B) so we can solve. Let's try to solve for B...

Answer 40

Ok

Answer 41

In you rfirst equation A+ B = 6000 how can we show it as an equation where B= (something)

Answer 42

Move A to the other side right?

Answer 43

Correct..subtract A form both sides and what do you have?

Answer 44

So A-A+B=6,000-A?

Answer 45

B=6,000-A

Answer 46

Great now we have B=6000- A....now look at your second equation of .07(A) + .09(B) = 500..we are going to solve by substitution so what can we substitute based on our first equation

Answer 47

I made an error earlier we are going to solve for A...

Answer 48

Oh then just the opposite

Answer 49

A=6,000-B

Answer 50

No

Answer 51

We have the equation .07(A) +.09(B) = 500 and we know B= 5000-A..we simply substitute the value we have determined for (B) into every value for B in the equation .07(A) + .09(B) =500....

Answer 52

Oh wait we had it right at first?

Answer 53

So you end up with .07(A) + .09(5000-A) = 500...do you see where I substituted?

Answer 54

Yes

Answer 55

Now distribute

Answer 56

Very good and solve for A

Answer 57

Kk give me a minute to solve it

Answer 58

Ok so A=2,000

Answer 59

So now we substitute that into A+B=6,000

Answer 60

To solve for B?

Answer 61

yes

Answer 62

So the answer for B is 4,000?

Answer 63

Very good...you can always verify your answers by plugging them into both equations and making sure they work...Great job

Answer 64

Ok and 1 more quick thing

Answer 65

ok

Answer 66

When we did a problem in class the answer came out to 18 quarters and my teacher said I had to put it into dimes as well someone immediately said 32 dimes and he said that is correct then class ended so I didn't know how he got that... How exactly did he get 32?

Answer 67

Unless I saw the problem I could not tell you because 18 quarters do not equal 32 dimes. I am sure this is another substitution problem as coins are often used. Do you have the problem handy?

Answer 68

Yeah I got it right here I'll type it

Answer 69

A person has 50 coins in dimes and quarters with a combined vaule of 7.70. Determine the number of coins of each type.

Answer 70

So waht are your two equations going to look like....let D= dimes and Q = quarters.

Answer 71

Well what I did was value+value=total value because we had a similar problem that we had to do the that

Answer 72

So I put down 25x + 10(50-X)= 770

Answer 73

Wait I am stupid

Answer 74

Nvm I figured it out

Answer 75

No you are on the right track..

Answer 76

I never thought of this lol 18+32=50....

Answer 77

That's how he got 32....

Answer 78

Well X=18

Answer 79

I feel really really really dumb

Answer 80

Never feel like that you do well....sometimes it takes a second to see it

Answer 81

Yeah just to make sure I did this right

Answer 82

It's the same kind of problem I asked at first

Answer 83

I just wanna make sure I have it down

Answer 84

You invested a total of $30,000 in two funds earning 8.5% and 10% simple interest. During 1 year, the two funds earned a total of $2,700 in interest. How much did you invest in each fund?

Answer 85

So same concept

Answer 86

A+B=30,000

Answer 87

Exact same

Answer 88

Does it really matter which I solve for at first?

Answer 89

Say if I want to solve for A this time does that really matter?

Answer 90

No

Answer 91

So I can do A or B

Answer 92

Yes but what will your second equation look like?

Answer 93

.085A+.10B=2,700

Answer 94

Correct..

Answer 95

Ok! Thank you so much!

Answer 96

If I have another problem think you could help? But the rest of the problems are pretty simple...

Answer 97

Always glad to help...on the coin question I just wanted to make sure that you have that set up correct...It is based on the number of coins so your two equations should look like this.... D + Q = 50 and .10(D) +.25 (Q) = $7.70 where D and Q represent the number of each coin...

Answer 98

What is the other problem