Question

EVERYONE GIVE @PHI A MEDAL BECAUSE HE HELPED ME FOR TWO HOURS! HE DESERVES IT!

Answer 1

Name the two funds.

Answer 2

Let x be 5%?

Answer 3

Let y be 3.5%?

Answer 4

Let's work on that just a little.

Let x be the amount invested at 5%
Let y be the amount invested at 3.5%

Do you agree that this sounds more descriptive of exactly what is meant?

Answer 5

yes. Thank you for helping me by the way and not just telling me the answer.

Answer 6

so... x+y=413

Answer 7

This is why we wrote very clear definitions.

x and y are amounts invested. They are NOT interest earned.
413 is interest earned.

Thus, x+y CANNOT be 413. They are just not the same thing.

We do have a total invested of $10,000.

x + y = 10,000

Now, let's talk about interest earned. Do you follow so far?

Answer 8

x+y=10 000
interest earned is $413..in a year.

Answer 9

Okay, how do we use x and y to talk about Simple Interest Earned. We already established that just adding them gives the total amount invested. How shall we use them to give the total interest earned?

Answer 10

10 000-x+y=413?

I'm sorry i'm not really understanding.

Answer 11

When in doubt, go read the very clear definitions.

Let x be the amount invested at 5%
Let y be the amount invested at 3.5%

What, then, is the amount earned by fund x?
What, then, is the amount earned by fund y?

Answer 12

x+y=413...

wait. out of 10 000 dollars, 5% of it is x. 3.5% of it is y.

Answer 13

x+y=10 000

Answer 14

You did not answer my questions. We already said x+y = 413 is very wrong. Amounts invested are NOT interest earned. Just answer my questions.

What is the amount earned by fund x?
What is the amount earned by fund y?

Answer 15

5% for x and 3.5% for y?

Answer 16

What exactly is interest?

Answer 17

No, 0.05 (5%) and 0.035(3½%) are the RATES at which funds are invested. That is not the amount that is earned.

You should have this formula, I = Prt, or Interest equals Principal multiplied by the Interest Rate multiplied by the time required. Interest is defined in this way. This requires an understanding of the other three terms.

P = the Principal earning interest. In our problem, this is x and y as we have defined them.

r = the Interest RATE that is earned or paid. In out problem, these are 0.05 and 0.035 as given in the problem statement.

t = the length of time of the investment. The problem statement tells us that this is One Year.

It is time to answer the two questions:

What is the amount earned (the interest calculated) by fund x?
What is the amount earned (the interest calculated) by fund y?

Answer 18

I have never seen that formula in my life.

Answer 19

Well, now you have. One has to wonder why you have been given such a problem if you have no such exposure. Is this a placement exam? If it is a placement exam, you should get this one wrong so that you are placed in the correct class.

Answer 20

If you want to see an explanation on interest, see
http://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/interest-basics-tutorial/v/introduction-to-interest

Answer 21

This is just a question from my math textbook. But, I've never seen the formula. Can it not be done without the formula?

Answer 22

thanks @phi

Answer 23

Your question makes no sense. That IS the way to calculate Simple Interest. If you off-handedly decide to discard the only method of calculation as required by the problem statement, you cannot solve the problem or the problem does not actually exist. You can choose which of these dire outcomes is more palatable.

Answer 24

I'm sorry tkhunny. This question is too hard. I know the first equation, but I'm not able to figure out the second. I understand you are getting annoyed. You can leave if you wish, and maybe @phi can help instead

Answer 25

to answer this question, you should watch the first 5 minutes of the video. Can you do that ?

Answer 26

alright. I'll be back in five minutes. But isn't it wrong to learn something you haven't learned in class yet? Doesn't it misguide you?

Answer 27

ok. So I watched the first 5 minutes.

Answer 28

hey @tomhue do you want to help me with this hard question?

Answer 29

The main idea is "interest" is money the bank pays you to borrow your money

Answer 30

so Mengxi had 10 000 dollars to invest. does invest mean loan?

Answer 31

Simple interest is how they figure out how much they will pay you.

For example, 5% per year simple interest means they will pay you %5 of what you loaned them.

Yes, invest means loan in this case

Answer 32

ok. so Mengxi had a loan of 10 000 from the bank. At the end of the year, she had to pay the bank 10 000 + 413, the interest they asked for.

Answer 33

If you invest (or loan) $100 for one year at 5% simple interest rate, you will get back the original 100 plus 5% of 100 (which we calculate at 0.05*100= $5)

Answer 34

so 10 413. but she also had to give them .05 interest and .35 interest.

Answer 35

am i on the right track here or no?

Answer 36

try not to get confused. Mengxi loans the bank 10,000. The bank pays HER some money to keep that 10,000 for a year. the total they pay her is 413 (plus of course the original 10,000)

Answer 37

so 10 413

Answer 38

yes, but we just keep track of the interest, the 413

Think about this question: if you loaned x dollars to the bank for 1 year at 5% simple interest, how much interest will the bank pay you?

any idea ?

Answer 39

x+.05?

Answer 40

or i pay the bank that

Answer 41

Phi, how about we solve an easier question first? I think I'm getting ahead of myself.

Answer 42

1. Leanne works at a greenhouse. She needs to plant a total of 32 bulbs. two types of bulbs are available. She is asked to plant three times as many crocus bulbs as tulip bulbs. How many of each should she plant.

Answer 43

Let x be crocus
Let y be tulips

Answer 44

x+y=32

Answer 45

3x=y

Answer 46

you have to be careful about interpreting the English

the sentence
*** three times as many crocus bulbs as tulip bulbs.***
means you have more crocus bulbs than tulip bulbs
in other words, x is bigger than y (so 3x= y is not correct)

Answer 47

x=32-y
3(32-y)=y
96-3y=y
96=4y
24=y

Answer 48

what?

Answer 49

oh so it would be 3y=x?

Answer 50

yes x= 3y

Unfortunately, the English wording can be confusing... if you have twice as many crocus as tulips, then you c= 2t (or x=2y).
same idea if you have three times as many crocus as tulips

Answer 51

when I read these problems, I always ask... okay, which is the bigger amount. that helps to figure out is it x=3y or y=3x

Answer 52

other than that, you did the problem correctly

Answer 53

1. x+y=32
x=32-y
2. x=3y
32-y=3y
32=3y+y
32=4y
8=y
1. x+8=32
x=32-8
x=24

There are 24 crocuses and 8 tulips.

Answer 54

The english language is confusing :)

Answer 55

I have another question, do you have time?

Answer 56

ok

Answer 57

2. James looks in his TV cabinet an finds some old BETA and VHS tapes. He has 17 tapes in all. He finds that he has three more BETA tapes VHS tapes. How many of each type does he have?

Answer 58

Let x be # of Beta tapes
Let y be # of VHS tapes

Answer 59

1. x+y=17
y=17-x

2. x=y+3
x=17-x+3
x+x=17+3
2x=20
x=10

1. 10+y=17
y=17-10
y=7

James has 10 beta tapes and 7 vhs tapes

Answer 60

perfect

Answer 61

OH! I FOUND ANOTHER INVESTMENT ONE!

Answer 62

4. Rehman invests in his summer earnings of $3050. He invests part of the money at 8%/year, and the rest at 7.5%/year. After 1 year, these investments earn $242 in simple interest. how much did he invest at each rate.

Answer 63

to do these, you first need to know how to answer this:
Let's use $100 as an example. You give the bank $100
you want that $100 back after 1 year.
You also want an extra amount of 5% of 100 (the interest)
at the end of the year.

how much interest will the bank pay you after 1 year?

Answer 64

so we're giving the bank a loan?

Answer 65

The bank should give me back 105 dollars.

Answer 66

you can think of it that way... but people use different language.. you make a "deposit" or "open an account" but it all means the same thing: the bank has your money (and you don't)

Answer 67

The bank should give me back 105 dollars.

Yes. How did you figure that out ?

Answer 68

because .05 multiplied by 100 is 5. So 5 + 100 is 105

Answer 69

they owe me the initial amount and 5% extra

Answer 70

OK. and the amount 0.05*100 is called interest.

Next, if you invest (or deposit or loan) the bank x dollars at 5%, how much simple interest do you get after 1 year ?

Answer 71

x+.05

Answer 72

if x were $100, your formula x+0.05 would mean 100+0.05 = 100.05
which does not match the answer of 5.
try again.

Answer 73

what is *just* the interest for loaning the bank x dollars at 5% for 1year?

Answer 74

x+5%

Answer 75

when we did, what is the interest on $100 at 5% for 1 year, what did you get ?

Answer 76

OH! x(.05)

Answer 77

yes. Now you have the basics for answering the question

Answer 78

Wow! Thanks! so...I'll try to solve it.

Answer 79

so..
Let x be 8%
Let y be 7.5%

Answer 80

x+y=242

Answer 81

wait no. this is wrong

Answer 82

i already know what x and y

Answer 83

the question asks for
how much did he invest at each rate.

so x and y should be the amounts invested (loaned) at the different rates

Answer 84

so was my x and y right?

Answer 85

***
Let x be 8%
Let y be 7.5%
***
that is unclear. x is not 8%. x is the amount of money loaned to the bank at 8% interest. at the end of the year the bank will pay interest of 0.08*x

Answer 86

so x= .08
y= 0.075

Answer 87

no. Time to stop and figure it out. x and y are dollars (not percents)
x+y is the total dollars given to the bank

Answer 88

I'm confused again...just when I thought I got it.

Answer 89

There are 5 numbers:
$3050
$242
1 year
7.5%
8%

Answer 90

You will get it... review these thoughts:
what is *just* the interest for loaning the bank x dollars at 5% for 1year?

Answer 91

but there are two different interests...

Answer 92

You will get it... review these thoughts:
what is *just* the interest for loaning the bank x dollars at 5% for 1year?

Answer 93

he gave the bank 3050

Answer 94

yes, but answer the question
what is *just* the interest for loaning the bank x dollars at 5% for 1year?

Answer 95

what do you mean by just?

Answer 96

x(.05)

Answer 97

good. now answer this question
what is the interest for loaning the bank x dollars at 8% for 1 year?