Hello:

1. If 63 books cost $126, what will 125 books cost?

Calculation: ($126 X 125)/63

Explanation: If 63 books cost $126, each book will cost one sixty-third of $126, which is expressed by 63 below the divisor line. 125 books will cost 125 times this number of dollars, which is expressed by writing 125 above the line as a factor of the dividend. The result is $250.

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If 15 men can do a piece of work in 7 days, in how many days can 21 men do the same work?

2. I think the calculation is (15 X 7)/21

Can you use a similar explanation from the first example to explain how the answer is determined for the second example?

Which would be used (1/21 X 15 men or 1/21 times 7 days) or neither?

I thank you for your reply and answer.

1. is correct but you should pay more attention to the units.

Use cost/book * number of books

thus $126 cost /63 books * 125 books

You get the same answer and the units are $

2. Same deal days/men * men = days

Try #2 again.

Hello:

1. If 63 books cost $126, what will 125 books cost?

Calculation: ($126 X 125)/63

Explanation: If 63 books cost $126, each book will cost one sixty-third of $126, which is expressed by 63 below the divisor line. 125 books will cost 125 times this number of dollars, which is expressed by writing 125 above the line as a factor of the dividend. The result is $250.

---------------

If 15 men can do a piece of work in 7 days, in how many days can 21 men do the same work?

2. I think the calculation is (15 X 7)/21

Can you use a similar explanation from the first example to explain how the answer is determined for the second example?

Which would be used (1/21 X 15 men or 1/21 times 7 days) or neither?

I thank you for your reply and answer.


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KeepItStupid - Reply

1. is correct but you should pay more attention to the units.

Use cost/book * number of books

thus $126 cost /63 books * 125 books

You get the same answer and the units are $

2. Same deal days/men * men = days

Try #2 again.

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How do I know which number to use as the numerator, 15 or 21?

Try #1 this way.

Let X= cost per book.

Then $126/63 = X - - X= $2.00

125 * 2 = $250

15 and 7 belong together, it's a ratio with either days/men or men/days depending on how arranged.

So 15 men / 7 days or 7 days / 15 men.

Your also given 21 men and you need to have units of days,

Thus,

7 days / 15 men * 21 men

Men divided by men gives you 1 with no units. This means that the men units cancel.

This 7/15 * 21 gives units of days

I'm a little confused... is that whole a single question? I mean, it is a whole where it shows you the difference between a direct proportionality and an inverse proportionality?

Anyway, the second problem is something completely different. Logically, if you have more men on a certain work, they'll complete it earlier that with fewer men.

1 man to build a house takes long time, but 10 men to build that some house takes much less time.

Say 3 men take 3 hours to clean a yard. You need to find the time that 5 men would take.

You use the inverse relationship:



Giving :

Using the given values, you find that k = 9.

Now, using the formula with k = 9 and Man = 5, you get the time as 9/5, or 1.8 hours which is logical since it takes less time for more people to do the same task.

So, looking back at your question, you the working well, and I gave you the explanation with an exmple. Now, you only need to put it in your own words for it to be corrected. :)

Except that the problem is situated somewhere else, where another logic is to be used since it's not a direct relationship, as I posted in the other thread.

KWF, try posting in the same thread if your want to have a reply to the ones answering you on one particular question. I's confusing when you have several threads concerning the same issue.

This is for Keepitsimple:

I want to thank you for your reply. I'm new to this site, and I do not know how to thank or comment on the reply by the expert. Perhaps you may know so that I can rake your reply.

Last reply:

15 and 7 belong together, it's a ratio with either days/men or men/days depending on how arranged.

So 15 men / 7 days or 7 days / 15 men.

Your also given 21 men and you need to have units of days,

Thus,

7 days / 15 men * 21 men

Men divided by men gives you 1 with no units. This means that the men units cancel.

This 7/15 * 21 gives units of days
Comments on this post
__________________

Check the post I made on your other thread, the very first you posted on here. To reply, type in the 'Answer this question' box and click on post quick answer.

This is another case, not the same as the first problem.

Thanks.

You can't rate an answer right away after you become a member. Some features of the site kick in after you have been a member 24 hours.

Since this thread was all related you should have just typed in the box and hit the "post quick answer".

Pretend it says to "Post reply to this topic". It's confusing to the OP (Original poster).

Go Advanced allows you to post certain file types directly and use smiley faces etc.

I will ask that your threads be merged.

For keepitsimple: The units cancel properly but the calculation 7 days/15men X 21 men is not correct.
It is 7 days/21 men X 15 days = 5 days. I thank you for your replies and help nevertheless.
For Unknown008 Thanks for the reply I have not seen that mathematical sign that you used, but I understand the inversion.

Kiss,

Before my network just went toes up, I was trying to post this formula

(days x men)= mandays/men

(7 * 15)/21 will yield 5 man days. (7 *15) = 105 /21 = 5

Thanks donf for the formula--sorry about your network.

Quote:

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Originally Posted by KWF

For Unknown008 Thanks for the reply I have not seen that mathematical sign that you used, but I understand the inversion.

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Actually, that was meant to mean 'is proportional to' and is in fact a little more stretched horizontally. When you remove that sign of proportionality, you have to insert a constant. You'll be surely using this concept much, later on.

If you don't want to find the constant, you can still use the method.



Without finding the constant, the first instance of time and men must equal the product of time and men at the second instant.

That brings you to the same result again, (15*7)/21

You're welcome! :)

I would set up the proportion to read:

M2 : M1 = T1 : T2
(21) : (15) = (7) : (X)
(15 * 7)
( 105 )
(21 * X)
( 21X )

21X = 105
X = 105/21
X = 5

21 : 15 = 7 : 5
(15 * 7) = 105
(21 * 5) = 105

(:)) Many thanks to Sr. Anne Regis - Dominican Nun at Holy Spirit Elementary School in
The Bronx, N.Y. (:))