Hi guys,

This is the question....if 7 dogs consume 3 bags of food in 12 weeks, how many weeks will it take 10 dogs to consume 3 bags?

Now this is common sense, what I would do is to say 7 dogs consume in 12 weeks, so 1 dog would consume in 84 weeks (12x7), the 3 bags, so 10 dogs would consume 10 times faster, which means 84 weeks devided by 10, which is 8.4 weeks.

How could I present this mathematically?..

juriemagic Oct 9, 2017

#1**0 **

I did it the same way as you Juriemagic.

You have done it mathematically, BUT

I do understand what you are asking but I am not all that good at these either.

CPhill does lots of these on the forum. He'd give you a good answer I expect.

Alan or Geno or Hectictar might give you a good answer too :)

Melody Oct 9, 2017

#2**0 **

7: 10 dogs = 3:3 bags = 12:D weeks

D=(7/10) / (3/3) x 12

D =7/10 x 3/3 x 12

D =252 /30

**D =8.4 Weeks.**

Guest Oct 9, 2017

edited by
Guest
Oct 9, 2017

#5**0 **

You may Juriemagic but I certainly don't.

Guest has rearranged the numbers so that they spit out the right answer but there is no explanation given as to why he/she is doing anything. In fact there is not logical flow of the algorithm.

I suspect he/she has no understanding at all.

Melody
Oct 9, 2017

#6**0 **

oops!!..then I guess that says a lot about me too!!!...lol.

Melody, yes, I certainly do understand what you are saying. Well, looking at this it certainly calculates to the correct answer. I kind of understand the principle behind this which was to take the first scenario and devide that by the 2nd scenario, making sure the unknown is at the bottom, meaning this:

\({7 \over10}:{3 \over3}:{12 \over x}\)

Then multiply the X out and put that equal to the rest. Multiply the top row and devide by the product of the bottom row.

anycase, I know you know what I'm saying, so it's not like I have to explain this to you..(sorry)..uhm, I think to really test this out would be to create a few different scenarious and try to calculate the unknown using this approach.

Thanx for being out there!!

juriemagic
Oct 10, 2017

#7**+1 **

Yea, it appears to me to be a simple proportion problem (I'm not he/she that came up with it)!.

7 x 3 x 12 =10 x 3 x W(weeks), solve for W.

Divide both sides by 10 x 3

W =[7 x 3 x 12] / [10 x 3]

W = 252 / 30

W = 8.4 weeks!.

Note: If you had twice as many dogs or 14 dogs, you would expect the time to be halved from 12 weeks to 6 weeks, and that is exactly what you get when you substitute 14 dogs instead of 10!.

Guest Oct 10, 2017

#8**+1 **

Actually this makes sense.

This is the question....if 7 dogs consume 3 bags of food in 12 weeks, how many weeks will it take 10 dogs to consume 3 bags?

When you are working our problems, usually rates problems, you can use the units to help you work out what you need to do.

here 7dogs*3bags*12weeks = 7*3*12 dogs bags weeks

The units are **dogs bags weeks**

So yes, this must equal

10dogs*3bags*y weeks = 7*3*y dogs bags weeks

7*3*12 = 10*3*y

etc :)

I have not used this units method for a question quite like this before. ://

Try it on a few different questions, I mean just change the numbers around and check it works Juriemagic. :)) I think you will find that it does.

Using the units in questions is often extremely helpful.

Melody
Oct 10, 2017

#10**+1 **

Thanx a lot Melody,

Like you said...this does make sense!. Thank you for your input!!

juriemagic
Oct 10, 2017

#11**+1 **

Here's my approach

If 7 dogs consume 3 bags of food in 12 weeks.....then they must consume 1/4 bag in one week

Which means that 1 dog must consume 1/7 of this = 1/28 bag in one week

So 10 dogs will consume 10 * 1/28 bags in one week = 5/14 bags of food per week

So....to consume 3 bags it will take 10 dogs

3 bags / ( [ 5 /14] bags per week) = 42 / 5 = 8.4 weeks

CPhill Oct 10, 2017