700-800 Formula Problem on CAT#2

[skyjarrett12]

I'm totally lost on this one: Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?

The explanation talks about "unique lengths" of the segment. I'm just completely lost and don't understand the explanation. Can someone please break this one down for me please?

[tim]

rather than going through an explanation you didn't feel comfortable with, let's have you tell us how you approached the problem and where you got stuck. then the explanation we give will make much more sense to you..

[allegro2012]

Lemme try this

One meter thirds -- 33.33,66.66,100

One meter fifths -- 20,40,60,80,100

So the total lenghts are -- 20,13.33,6.66,20,6.66,13.33,20

what is the ask on the question??

[jnelson0612]

I'm totally lost on this one: Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?

The explanation talks about "unique lengths" of the segment. I'm just completely lost and don't understand the explanation. Can someone please break this one down for me please?

Hi Sky!
We did one like this one in class (but it's been awhile). :-)

Let's first consider that since we are breaking the branch into thirds and fifths, we should get a common denominator of 15 for all of our fractions. Thus:
1/3=5/15
2/3=10/15

1/5=3/15
2/5=6/15
3/5=9/15
4/5=12/15

Now, draw out a number line from 0 to 15. Note the points where you have breaks: 3, 5, 6, 9, 10, 12.

What are the sizes of pieces of you have?
0-3 = 3 meters
3-5 = 2 meters
5-6 = 1 meter
6-9 = 3 meters
9-10 = 1 meter
10-12 = 2 meters
12-15 = 3 meters

The question says that I remove a piece of each distinct (different) length. So let's see, I have three different lengths: 1, 2, 3. If I take out one of each of those lengths, I take out 6 total meters of length. What is left of the 15 meters? 9 meters. Thus, 9/15 or 3/5 remains.

Let us know if any of this doesn't make sense.

[allegro2012]

Jamie -- can you please explain where the approach that I was taking was going wrong.

Thanks

[RonPurewal]

Jamie -- can you please explain where the approach that I was taking was going wrong.

Thanks

nothing so far -- but you didn't proceed to answer the actual question.

the question was, "How much of the original branch was left after taking out one piece of each of the different lengths?"
the way you've analyzed this, the different lengths are 6.67, 13.33, and 20. if you have one of each of these lengths, the total length is 40.
remove 40 from 100 and you have 60 left over. that's 60/100 = 3/5 of the total length.

[allegro2012]

Ron -- Thanks for the insight.. I just could not figure out what the ask was.

Now i understand the question.

[tim]

:)

[skyjarrett12]

Jamie -

Thanks so much for this explanation! That really spells it out nicely! I was even able to explain it to my boyfriend!!! Any hints on where I could similar questions like this to practice with?

[tim]

be careful trying to find too many "similar" questions, as that will lead you to memorizing a ton of very specific formulas that will not be of much use. just continue working on nonstandard problems and remember there is not always a formula because a lot of these just require you to think your way through what is being asked and how to work out a solution on your own..