Easy peasy math problem

[DB5]

Hi folks,

I anticipate that the following math problem will be quite easy for some of you, but that is not the case for me, so I kindly request your assistance:

There were 247 requests for a cookie by students in a school cafeteria over the course of 3 months. Of those 247 requests, the average over the 3 months was that 95.9% resulted in approvals.

How many requests for a cookie are represented in the 4.1% of denials?

Cheers,
Daniel

 

[Deleted member 4993]

Hi folks,

I anticipate that the following math problem will be quite easy for some of you, but that is not the case for me, so I kindly request your assistance:

There were 247 requests for a cookie by students in a school cafeteria over the course of 3 months. Of those 247 requests, the average over the 3 months was that 95.9% resulted in approvals.

How many requests for a cookie are represented in the 4.1% of denials?

Cheers,
Daniel

What is 25% of 100?

What is 50% of 10?​

What is 75% of 1000? - How did you calculate that? Follow the exact same procedure.​

What is 4.1% of 100? What is 4.1% of 247?​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[DB5]

Hi Khan,

Cheers for the engaging response, I will attempt to answer the 6 questions posed:

(1) 25.
(2) 5.
(3) 750.
(4) I calculated that by a process of basic math, one might say "easy peasy", even. OK.
(5) 4.1.
(6) ??? -- stuck mode!

Cheers, D

 

[The Highlander]

Hi folks,

I anticipate that the following math problem will be quite easy for some of you, but that is not the case for me, so I kindly request your assistance:

There were 247 requests for a cookie by students in a school cafeteria over the course of 3 months. Of those 247 requests, the average over the 3 months was that 95.9% resulted in approvals.

How many requests for a cookie are represented in the 4.1% of denials?

Cheers,
Daniel

The question you have quoted describes a situation that is not possible!
Because "requests" are discrete (not continuous) data. ?
ie: there cannot possibly have been 95.9% resulting in "approvals".

 

[lev888]

The question you have quoted describes a situation that is not possible!
Because "requests" are discrete (not continuous) data. ?
ie: there cannot possibly have been 95.9% resulting in "approvals".

7 out of 8 is 87.5%. Integer quantities may correspond to fractional percentages.
Edit: I guess you were referring to the result of applying that percentage. Maybe the fact that it's the average explains it?

 

[BigBeachBanana]

The question you have quoted describes a situation that is not possible!
Because "requests" are discrete (not continuous) data. ?
ie: there cannot possibly have been 95.9% resulting in "approvals".

If you re-read the OP, it's "the average over the 3 months...", thus it's not necessarily required to be integers.

 

[lev888]

If you re-read the OP, it's "the average over the 3 months...", thus it's not necessarily required to be integers.

Still don't get it. I would expect fractions if the average were applied to a single month's amount. But the total approved should be an integer.
E.g.:
50% average approval rate
Monthly total amounts: 3, 3, 4
Approved: 1, 2, 2.
Percentages: 33.333%, 66.666%, 50%
If average % is used: 1.5, 1.5, 2 - ok to have fractions.
Total approved: 5 - has to be an integer.

 

[BigBeachBanana]

Still don't get it. I would expect fractions if the average were applied to a single month's amount. But the total approved should be an integer.
E.g.:
50% average approval rate
Monthly total amounts: 3, 3, 4
Approved: 1, 2, 2.
Percentages: 33.333%, 66.666%, 50%
If average % is used: 1.5, 1.5, 2 - ok to have fractions.
Total approved: 5 - has to be an integer.

Maybe what I said didn't come out correctly. What I meant is exactly what you said, it's ok to have a fraction for the average %.

 

[Deleted member 4993]

(4) I calculated that by a process of basic math, one might say "easy peasy", even. OK.

What operation/s of basic math (addition, subtraction, multiplication, division) you had used to arrive at the answer.

Please show us the steps (your thought process) to arrive at the output of 750 from the given input of 1000 and 75%?

 

[DB5]

1000 = 100%
100 = 10%
10 = 1%
:. 75% of 1000 = 750

...it would be both helpful and beneficial if someone was to provide the answer so I could see how to the arithmetic the other way.

Cheers,
DB

 

[Otis]

1000 = 100%
100 = 10%
10 = 1%

Hi DB. Those equations are not true. However, the following equations are true.

1000 = 100% of 1000
100 = 10% of 1000
10 = 1% of 1000

Are those what you meant to type?

In other words, when we take a percent of a whole, we get the specific percentage.

percentage = percent of the whole

750 = 75% of 1000

The percent is 75%, the whole is 1000, and when we take 75% of 1000 we get the corresponding percentage: 750.

If you'd like to write equations to show arithmetic values for specific percents (that is, to show the numbers used for calculating percentages of wholes), then the equations would look like this:

1 = 100%
1/10 = 10%
1/100 = 1%

In other words, one-tenth of something is 10% of that thing.

And, one-hundredth of some quantity is 1% of that quantity.

Therefore, 75% of a number is 75/100ths of that number.

When doing arithmetic with percents, we use the numbers 1/10 or 1/100 instead of 10% or 1%. We may work with those rational forms (fractions) or we may work with the decimal forms.

1% = 1/100 = 0.01

Therefore, to calculate 1% of 355, we may do either of the following.

[imath]\frac{1}{100} \times 355[/imath]

[imath]0.01 \times 355[/imath]

Likewise, for calculating 75% of 355, the arithmetic could be done either way.

[imath]\frac{75}{100} \times 355[/imath]

[imath]0.75 \times 355[/imath]

You mentioned "the other way" to do the arithmetic. I'm not sure what you had in mind. If I haven't addressed that question, could you explain or show a sample? Thanks.

[imath]\;[/imath]

 

[The Highlander]

7 out of 8 is 87.5%. Integer quantities may correspond to fractional percentages.
Edit: I guess you were referring to the result of applying that percentage. Maybe the fact that it's the average explains it?

If you re-read the OP, it's "the average over the 3 months...", thus it's not necessarily required to be integers.

Of course discrete data can produce fractional percentages, I wasn't suggesting they can't! I was simply pointing out that no fraction of 247 discrete data can equate to 95.9%.

Nor could I find a combination of monthly results that would produce an "average" (mean, I assume) over 3 months that equates to 95.9%!

Can anyone else?
(I will happily stand corrected if anyone can! ?)​

Notwithstanding that, it's probably likely that whoever authored this question wasn't particularly concerned about the 'accuracy' of their figure(s) but simply wished to present 'candidates' with practice in working with fractional percentages of quantities that are not rounded to 10s or 100s?

(So it's probably not worth 'agonizing' any further over the question's arithmetic ‘consistency’ ?)

...it would be both helpful and beneficial if someone was to provide the answer so I could see how to the arithmetic the other way.

We don't give out the "answer" here (especially to such "Easy peasy math" problems ?); the clue is in the name (freeMATHhelp). We are happy to offer advice on how to improve your efforts or make suggestions that might encourage you to find the answer(s) for yourself.

On that basis, have you tried this method of finding percentages?

Find 1% of your quantity by dividing by 100,
(eg: insert a decimal point and then move all digits 2 places to the right),
then simply multiplying that result by the percentage fraction you wish to calculate.

For example, to find 3.2% of 274:-
1% of 274 = 2.74
so, 3.2% of 274 = 3.2×2.74 = 8.768 ≈ 9 (ie: to the nearest whole number.)
(That's as close to an "answer" as you're likely to get! ?)

Now, have another go at your problem and let us know how you got on.

 

[Steven G]

Example: What is 13% of 80.
% means divide by 100, ie /100
of means to multiply, ie *
13% of 80 = \(\displaystyle \dfrac {13}{100}*80 = ...\)

 

[DB5]

Hi DB. Those equations are not true. However, the following equations are true.

1000 = 100% of 1000
100 = 10% of 1000
10 = 1% of 1000

Are those what you meant to type?

In other words, when we take a percent of a whole, we get the specific percentage.

percentage = percent of the whole

750 = 75% of 1000

The percent is 75%, the whole is 1000, and when we take 75% of 1000 we get the corresponding percentage: 750.

If you want to write equations that show the meaning of isolated percents (that is, stating a percent without stating a whole or a percentage), then the equations would look like this:

1 = 100%
1/10 = 10%
1/100 = 1%

In other words, one-tenth of something is 10% of that thing.

And, one-hundredth of some quantity is 1% of that quantity.

Therefore, 75% of a number is 75/100ths of that number.

When doing arithmetic with percents, we use 1/10 or 1/100 instead of 10% or 1%. We may work with those rational forms (fractions) or we may work with decimal forms.

1% = 1/100 = 0.01

Therefore, to calculate 1% of 355, we may do either of the following.

[imath]\frac{1}{100} \times 355[/imath]

[imath]0.01 \times 355[/imath]

Likewise, for calculating 75% of 355, the arithmetic could be done either way.

[imath]\frac{75}{100} \times 355[/imath]

[imath]0.75 \times 355[/imath]

You mentioned "the other way" to do the arithmetic. I'm not sure what you had in mind. If I haven't addressed that question, could you explain or show a sample? Thanks.


[imath]\;[/imath]

Otis, cheers for the engagement, I very much appreciate it! I feel that you have addressed my question so comprehensively, that it amounts to work which requires close inspection and further study for me.

 

[DB5]

Example: What is 13% of 80.
% means divide by 100, ie /100
of means to multiply, ie *
13% of 80 = \(\displaystyle \dfrac {13}{100}*80 = ...\)

Master Steven, thank you, that is an example of assistance which I can now use to reply with the following answer:

What is 4.1% of 247 where:
(i) % means divide by 100, ie /100; and
(ii) of means to multiply by, ie -
4.1% of 247 = \(\displaystyle \dfrac {4.1}{100}*247 = ...\)

Am I correct by supplying the answer that: 1.6 requests for a cookie were not approved?

 

[AvgStudent]

Master Steven, thank you, that is an example of assistance which I can now use to reply with the following answer:

What is 4.1% of 247 where:
(i) % means divide by 100, ie /100; and
(ii) of means to multiply by, ie -
4.1% of 247 = \(\displaystyle \dfrac {4.1}{100}*247 = ...\)

Am I correct by supplying the answer that: 1.6 requests for a cookie were not approved?

My calculator tells me that \(\displaystyle \dfrac {4.1}{100}*247 = 10.127\)

 

[Steven G]

My calculator tells me that \(\displaystyle \dfrac {4.1}{100}*247 = 10.127\)

You got it!

 

[Deleted member 4993]

How many requests for a cookie are represented in the 4.1% of denials?

The answer should be an integer - like 10.

Then you need to check whether the answer is approximately correct or not by finding 10/247 and comparing it with 4.1%.

 

[The Highlander]

The answer should be an integer - like 10.

Then you need to check whether the answer is approximately correct or not by finding 10/247 and comparing it with 4.1%.

I'm afraid that may confuse matters further. ?
As I pointed out above, the numbers in the original problem haven't been very judiciously chosen by it's author as they are, in fact, not possible with discrete data like this. ?
It's almost certainly the case that the answer sought is, in fact, 10 (an integer value just as you point out) but your suggestion to "check" this will not produce the "desired" result (of 4.1%) because it very much looks like this problem has just been authored as a means to provide practice in calculating fractional percentages of 'large' quantities without paying any attention to the arithmetic consistency of the numbers involved. ?

 

[Deleted member 4993]

I'm afraid that may confuse matters further. ?
As I pointed out above, the numbers in the original problem haven't been very judiciously chosen by it's author as they are, in fact, not possible with discrete data like this. ?
It's almost certainly the case that the answer sought is, in fact, 10 (an integer value just as you point out) but your suggestion to "check" this will not produce the "desired" result (of 4.1%) because it very much looks like this problem has just been authored as a means to provide practice in calculating fractional percentages of 'large' quantities without paying any attention to the arithmetic consistency of the numbers involved. ?

I agree and that is why I used the term "approximately" .