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Melody

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Melody  11 feb 2022
 #41
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Hi Random,
I am glad that you are still with me,

This was the question:
The bananas are bundled in nets of 2 (2 bananas per net)
The cost is $4.08 for a dozen. And I want 14 bananas.
a) How many nets make up a dozen bananas Your answer: 12/2 = 6 Perfect!
b) If r is the cost per net, what is r ? Your answer: Not so good
c) If n is the number of nets that I need to buy, what is n? Your answer: 7 good.


Your answer for part b
b) 14/4.08 = 1 banana
so 1 banana= 3.43
so 3.43 x 2 = $6.86 per net

Lets think about this.
If 1 banana was $3.43 then a dozen bananas would be $3.43 x 12 = $41.16 BUT a dozen bananas are only $4.08, so your $3.43 per banana can't be right.
Think about the words and use them to help you get these sorts of questions correct.
If you want dollars per banana You have 4.08 dollars per 12 bananas.
The per is the same as divide.
so you have
4.08/12 dollars per banana = $0.34 per banana = 34c each
check 12 x 34c = 408c = $4.08 so they must be 34c each!
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I'll get back on track later but this is really important for you to know.
REMEMBER: It is "cost per item"
a) If I buy 250 lollypops for $10. How much are they each (Show your working - that is the important bit)
show me how you checked your answer
b) If I buy a dozen eggs for $6.48 How much is each egg (Show your working - that is the important bit)
show me how you checked your answer.

Please answer these 2 questions for me.
30 dic 2013
 #39
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Not there yet.
But if you are as persistant as I am you will eventually tell me that you totally understand. And, when i give you questions that you can do easlily, I will believe you.
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I want to try something new.
You are in a greengrocers shop.
All the produce is bundled up in those little nets. You know, like the ones you often buy onions in.
Are you with me so far?

Now, all the apples are bundled into groups of 3. That is, every apple net has three apples in it.

Above the apples is a price sign. It says $6 for 1 dozen apples. I want 2 dozen apples.

Let r be the price of one bag of apples. How much would this be?
12 apples divided by 4 = 3 apples (This means that i will need 4 bags to make 1 dozen apples)
So if I divide $6 by 4 I will get the price of 3 apples. Does that make sense?
So r = $6/4 = $1.50
Let n is the number of bags I need to buy.
I want 2 dozen and there are 3 in bag.
4 bags would be 1 dozen
So i must need 2 x 4 bags of apples.
n = 2 x 4 bags

Now think about this carefully Random. I think that a part of your problem is that you are not thinking hard enough about what I am trying to tell you.
Do you completely understand what I have done? Tell me if you don't!

Alright I will assume that you understand.

so
If the cost is $6 for 1 dozen apples, I want 2 dozen apples, and the apples are bundled in nets of 3
(1 dozen apples = 4 nets)
so
I will need 2 x 4 nets of apples n=2 x 4
and I will have to pay 6 divided by 4 dollars for each bag r=6/ 4

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If you totally understand this you will have no problem answering this question.
The bananas are bundled in nets of 2 (2 bananas per net)
The cost is $4.08 for a dozen. And I want 14 bananas.
a) How many nets make up a dozen bananas
b) If r is the cost per net, what is r ?
c) If n is the number of nets that I need to buy, what is n?

Now don't get annoyed with me and don't go back to an earlier problem.
Just answer my questions exactly as I have asked them, and show your working- that's the important learning part.
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29 dic 2013
 #33
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I have put a great deal of thought into this answer and i have discarded an earlier version. I really want you to understand and you are nearly there.
however,
I am sorry you still haven't quite got it, the last question on simple interest was perfect (all except for the missing dollar sign)
Your second last question was correct and i am sure you had the right idea but it may have been better to have said something like
"With simple interest you only get interest on your original deposit. With compound interest you ALSO get interest on the interest that you have already earned.
Therefore you will get a smaller total if simple interest is used."
Part d and e would both have been right if the earlier parts had been correct.

This is an extract from your original question. All except I changed the capital R to a little r in the equation. It is always written as a little r.
This is the formula. We are doing compound interest the formula is A= P(1+r) n
A= Amount owing or earned at the end of the complete process
P= Principal
r= interest rate per compounding period expressed in decimal
n= Number of compounding Periods

As for the early bits, your main mistake is exactly the same mistake that you made before. Interest is stated as a yearly amount. It doesn't directly matter how many months are in a compounding period. What matters is how many compounding periods there are in a year.
If you concentrate on getting your r and n right the rest will be easy.
Just use the original formula that you were given A= P(1+r) n [this is the foumula that i wanted you to write down for part (a)]
r is the yearly interest rate split up into (divided by) how many times a year interest is paid.
n is the number of compounding periods which is the number of years multiplied by how many times each year the interest is paid.
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Okay now forget about the last question for a moment.
Try these questions - don't simplify the answers, you can leave them as a decimal divided or multiplied by something.

If interest was 14% p.a., (p.a. means per year) and the money was invested for 2 years
a) what would r be if it was compounded every 1 month? (Hint: how many 1month time periods are there in a year?) What would n be?
b) what would r be if it was compounded every 2 months? What would n be?
c) what would r be if it was compounded every quarter (3 months)? What would n be?
d) what would r be if it was compounded every 4 months ? What would n be?
e) what would r be if it was compounded every 6 months ? What would n be?
f) what would r be if it was compounded every day ? What would n be?

Please be patient with yourself and with me.
Even if you don't get it this time, I can explain this and you will eventually get all these questions correct
28 dic 2013