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Mountain height word problem

Using some basic algebra to solve what looks like a hairy word problem that involves proportions.
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Mountain height word problem

Discussion and questions for this video
in 7:44,i dont understnd the '1/5x have <1/5 yr cellphone.
That's because Sal made an error at 7:40 into the video. Sal says and writes, "One fifth x have less than one fifth year cell phone" when the problem states, "one in five of all students have a cell phone that is one year old or less." To be correct, Sal should have written "1/5 x have < 1 yr cell phone." Hope this helps. Good Luck.
In a nutshell, can some one please explain exactly what a proportion and ratio is? (In the simplest but most knowledgeable way please)
Ratio: The quotient of two quantities that are in the same unit.

Proportion: An equation stating that two ratios are equivalent.

:) (Hope this was Helpful!) (;
What are ratios and what do we use them for?
(This was my question when I was younger, I asked this question because I still haven't seen anyone ask this and I want to share my answer to those who are also curious)
Ratio means (or is defined as) the quotient of two numbers or quantities indicating their relative sizes.

The ratio of a to b is written as a:b or a/b. The first term a is called the antecedent, and the second term b is called the consequent

Ratios are used when there appears a need or utility to compare numbers of quantities with one another

Whenever there's a need to do comparisons numerically, we use ratios and proportions.
For example (I'll give you 3 examples):

a) We compare Frank's age with Bob's age. Frank is 24 years old, while Bob is 12 years old. Therefore we say that the ratio of Frank's age relative to Bob's, is the ratio 2:1 (we read that as : ratio two is to one) OR that proportionately,Frank is twice Bob's age.

b) When we learn in baking that for Aunt Linda's strawberry chiffon cake we would require 4 eggs for every 2 cups of flour, while for Grandma's recipe for butter and walnut cookies we would need 1 egg for every 2 cups of flour, then we could say that (comparing the number of eggs required for the cake in comparison with the number of eggs required to bake the cookies):
the ratio of eggs required for the cake relative to the cookies is 4:1 (four is to one) or that, in order to bake the strawberry chiffon cake properly we need 4 times the number of eggs required to bake the butter and walnut cookies,or 4/1.

c) Comparing the number of years two comets(Comet Klemola and Comet Encke) take orbiting the Sun, if the Comet Klemola orbits the Sun every 11 years while the Comet Encke takes 3 years (not the exact number, you would have to compute the exact period using its precise speed, but for purposes of illustration, let's just say 3 for convenience), then the ratio of the inner cloud orbit (the astronomical term for "orbiting around the Sun") of the Comet Klemola relative to Comet Encke is 11:3 or 11/3.

Ratios are used in obsevation of quantities as well as deriving and formulating quantities. Some of the interesting applications in both Physics and Chemistry are as follows:
1.) Creating new types of alloys, after comparing relative strengths of metals and their other properties
2.) Combining chemicals to form personal care products,after comparing the speed of the effects of various components on the skin (It's not as bad as it sounds...we're talking about adding oatmeal or Vitamin E to soaps and shampoos)
3.) Cooking and baking, after much expereimentation and comparison, to make for instance, a softer, more moist red velvet cake
4.) Probability and statistics (It gets interesting after you've compared your chances for accomplishing many things, given a specific time frame)

etc........
ratio is simialar to fratcions but not completly
I get it its pretty easy once you get the hang of it but sometimes when you have fractions you have to cross multiply
MOST IMPORTANTLY: Sal wants us to get why cross multiplying works! It's just looking under the hood of the engine. Don't worry cross multiplying is the engine, it will always work! -Cheers!
You have to divide the number 639 in three parts x, y, z in order that x:z = 5:6 and y:z = 8:9 ? how can i solve this problem?
It includes a lot of algebra, so it might be a bit complicated.
639= a*b*c (I just switched the letters, it makes it more convenient)
a= (5/6)c
b= (8/9)c
639= (40/54)c^3
862.62=c^3
9.51944..=c
7.93286924..=a
8.4617..=b
To answer your original question-
x= 7.9328..
y=8.4617..
z=9.5194..
x*y*z equals your number (639).
Please help! I want to prepare for next year in 6th grade. I hear you study this too. Can you help explain it for me?
Sal, please help with this question:
The ratio of Science and Arts students in a college is 4:3.If 14 Science students shift to Arts then the ratio becomes 1:1.Find the total strength of Science and Arts students.

How would you solve something like this?
There are 112 sci students and 84 art students.
Hope that helped! plz vote up!
The last word problem is frying my brain. If x = total number of students, why would you multiply the total number of students by 1/5, because the 1/5 only applies to those who have phones which is 2/3's of x.

I was thinking how to take 1/5 out of 2/3 and come up with this. If you divide 1/5 by 2/3 (multiply the reciprical) you get 3/10 <- number of students with new phones. Out of 10 students 3 have a new phone. So 7/10th have old phones or 7 out of 10. Is this another way of figuring out this problem? Sorry if this confuses anyone, I am very confused and I need to understand this. Thank you for lessons I need to watch more obviously.
I think you misunderstood the problem. It says 1/5 out of ALL students, not 1/5 out of students that have a phone.
Not really a question but,
Thanks you Sal for being such a lifesaver! Now I understand math!
LOL you know there is a comment section at the top below the video right? XD
at 5:31 the sun was awesome
Help please!! I don't understand how and why Sal is dividing 44/48 by 4800, when does this rule/option apply and why can that be multiplied by 44. Thank you!!
How does this all work out
Proportions are direct comparisons between two numbers.
They are only expressed using fractions.
At the very beginning, the first problem, I watched this part about 10 times. I still don't understand what you ares saying. My teacher said to use this website and I love it but some things are still really hard. Especially the proportions. Thank you.
Can someone please help me to understand what he did at 4:19? I understand that 4800 can be divided by 48 100 times but how is it possible to eliminate these two numbers simply because of this relationship?
Crossing these numbers out just means that he's doing the division there. Now that he's done, he doesn't need the numbers 48 or 4800, all he needs for the next step is the numerator of that fraction and the result of the other operation (100).
Why do the Xs cancel at 0:48?
If you multiply by x and divide by x, then you are multiplying by x/x which is 1, so you can just cancel them out.
What is the difference between ratio and proportion....... It's really getting me confused! Some please help........ Thanks :)
A ratio is a comparison between two equivalent numbers. A proportion is two ratios that are equal. And yes, they are very similar because they are both comparing numbers.
I need help...

I don't know whether to simplify the fractions and what should multiply fractions by (x).
example:
((x) x 13/6 = 5/(x) x (x))
Real Problem:
3/9 = y/21
In this situation, I would simplify the fractions and then cancel them out.

3/9=y/21 can simplify to 1/9=y/7

then you can multiply the demoninators together and get the answer.
At 6:36 Sal says it should be 4 less than 300. shouldn't it be 4 less than 600?
Yes, he made a mistake in what he said, but what he wrote was still correct.
how do you determine whether a pair of ratios form a proportion?
So all you need to do is cross multiply and thats how you do ratio?? I really dont get it that much. I will just do prctice on it and see what I can pull together on the video. Jklolfmao19,check me out on Call of Duty Modern Warfare 3 [MW3] for PS3 and Call of Duty Black Ops 2 for Xbox 360...BEACH!!
why did sal reverse the fraction 13/6 into 6/13 @ at the beginning??
When you multiply a fraction by itself, you have to multiply the original by the inverse, which is just the fraction flip upside down.

Make sense?
In problem 2 starting at 6:53 I still a little confused when divideing the different
varibles can someone please explain?
Thank You
There are 1,312 Students in a middle school. On any given day there may be 65 students missing. What is the percentage of students missing on any given day?

Is this the correct way to solve a problem like this?
65/1312 = x/100
1312x = 65(100)
1312x=6500
6500 divided by 1312x
is 4.95%

OR what is the other method of doing this problem? Like solve for x (aka the unknown percentage here)? Besides using proportions how would you go about correctly translating this problem? for example when it say "what is(equals) the percentage of(multply) missing students on any given day? I think it means, 65(P)=1312
or 1312(P)=65
That is correct. Your answer also makes sense because 10% of 1312 is 131, and 65 is a bit less than half of that.
Why didn't sal divide 67 to 4400
i don't know... :(
Wait... why do you 7/15(x) / 2/3(x) or 7/15(3/2) = 7/10 at the end? Question: Out of the students who own a cell phone, which is 2/3(x), what proportion owns a phone that is more than one year old/not 1/5(x)? so.. 2/3(x) - 1/5(x) = 7/15(x) <------Isn't that just the answer???? why are we doing the other stuff at the end of the vid?
Because the question is "what proportion owns a cell phone that is more than one year old out of the students *who own a cell phone*". It's not asking "out of *all* the students", which is what 7/15(x) is.
why did he say the answer for yukon is 4 less than 300 when i was 4 less than 600
I need some help solving this please?: 8/(x+3)=1/x +1
What does proportion mean again :D
What is the technical definition of a proportion? #confused
This discussion area is not meant for answering homework questions.
if 1/5 of the total students own a cellphone less than 1 year old then the no of students who have a cellphone older than 1 year should be 4/5 of the total number of students. right???
Not necessarily, because at 7:02 it says 1/5 have one less than a year, and since there are 5/5 students in all, then of the remaining 4/5s, there are still two groups: students who have a cell phone older than a year, and students who don't have a cell phone.
Why can't I use cross simplification on ratio equations? If 12/8 = x/9 why does it not follow that 1/2 = x/3?
How do a solve the following problem using proportions.
You want to meet your friend at a park 4 mi. away from your house. You are going to bike to the park at an ave. rate of 10 mi/hr. Your friend lives 1.2 mi. away from the park and walks at an average rate of 3 mi/hr. How many minutes ahead of you should your friend start out so that you meet at the park at the same time.
I can't solve it using proportions, but I can at least _try_ to solve it. First thing we need to figure out: how many minutes it's going to take for you to get to the park. If you travel at the rate of 10 mi/hr, then you'll go 10 miles in one hour. That's too far. All we have to do is multiply by 4/10 on both sides to get four miles in four tenths of an hour. That's four tenths of sixty minutes, or twenty-four minutes, the time you need to get to the park. If the friend lives 1.2 miles away from the park and they travel at 3 mi/hr, and since 1.2 is four tenths of 3, then they'll need the same twenty-four minutes to get to the park. Just look at the proportions:
4 / 10 : 1.2 / 3
4 / 10 : 12 / 30
4 / 10 : 4 / 10
So you'll need to leave at the same time to be there at exactly the same time.
Always happy to help with rate problems or whatever that was,
Jack Kiuttu
This video makes no sense to me. I need help ;[
Just don't let the equations sit there all lonely. It's hard to go straight up- you'll never convince a 2 on the bottom of 1/2 to climb over that roof. But diagnolly, any number can climb steps, even I can (and I weigh 220 lol). So Bring the lonely numbers from the bottom, to the tops diagnoly across, through the '=' elevator. Just make sure you do it to both numbers, or you end up with a very angry left out number, that will snitch on your teacher to get you marked wrong on the test!
I don't get the mountain question. How'd he get Ben Nevis's size?
For the mount Yukon problem... I don't see how he used the cross multiplication technique ... I just saw regular multiplying and dividing fractions. Did he use it? He started the video with cross multiplication so you would think he would use it in his word problems for examples. Am I missing something here?
help! i don't get this! HELP! :( !
cant i just use cross products to solve these problems. i mean thats what i am doing and it works.
why multiply by N or B in the ratio what the concept what the actual rule

he said Y=289/67 N why
how do u rewrite a quotient as s a ratio using the units in a denominator
What is 2.8 hours to 3 days? I changed days to hours and changed 2.8 to 2.48 hours then "x" by 100 to get a whole number but still don't understand.
Well, 3 days is 72 hours, right? So you have the ratio 2.8 : 72. One mistake you have is changing 2.8 to 2.48; you are correct in thinking that 0.8 hours is the same as 48 minutes, but it's completely unnecessary to change 2.8 hrs to 2 hrs 48 mins because that gives you two different units (hours and minutes) when, in order to solve the problem, you must have just one unit (hours), which is the reason you changed days to hours in the first place.
So, back to the problem, you have 2.8 : 72. You can multiply by ten to get 28 : 720. The greatest common factor of 28 and 720 is 4; dividing both numbers by 4, you get 7 hrs : 180 hrs.
i get it now..
can someone put a question for me to solve in the comments?
Please help, I am in desperate need!
9000+294750239570
I am really really really really really really really confused what do you mean?
i think i may have missed a video......
a man brought a house for Rs.5 lacs and rents it.He puts 12.5% of each month's rent aside for repairs, pays Rs.1660 as annnual taxes and 10% on his investment there after..The monthly rent of the house=??
if u take 227/12 and 375/3 could make a proportion out of it?????
It wouldn't be an equal proportion, so nope.
Do you have worksheets which would help me with ratio and proportion
If you are having trouble with any subject, the practice problems are a great solution.
a bag contains 20 kg of rice and another bag contains 60 kg of wheat, find the ratio of the amount of rice to that of wheat.what is the ratio of rice to the total weight ?
I need help solving this problem. Michael walked 6 miles in 40 minutes. How long did it take him to walk the first 2 miles?
well all you have to do is divisde. if he walked 6 miles in 40 minuets, then he must of walked 3 miles in 20. then l 1/2 miles in 10. then 1 in about 7.5. so it is 15 minuets
why do you have to put an x
You mean at the beginning? He is setting a problem, which he then works out. x stands for "some number".

The problem is, 13/6 = 5/"some number". What is the number?
why are we multiplying by nevis i understand nevis is same size but why multiply 2:55
plz answer
at about 4:21: why is 44/48 multiplied by 4800?
Ben Nevis is 44/48 size of Mount Blanc. To find out the size of Ben Nevis Sal needed to multiply Mount Blanc by Ben Nevis. In these ratios, Sal needs to find the height of Mount Yukon. In order to do so, he needs to work backwards to get the height of each mountain to answer the following question.

To get the answer for E= 220/67 N Sal needs to get the answer for E=44/48 B and Sal already knows that B= 4800.

```E= 44/48 * 4800 (to see work watch the video from 4:03 to 4:36)```

Hope that helps!!
the magic that Sal used can also be cross multiplied then it is a basic equation problem.ex.
13/6=5/x 13.x=5.6
in a camp 180 students had ration for 20 days. how many students should leave the camp so thatthe same ration may last for 25 days?
30 students should leave the camp.... :)
I am having a hard time understanding this, especially since Sal made a mistake at 7:36. Maybe I need to figure it out on my own?!
It takes Joaquin 1/5 hour to hike 1/4 mile. What is Joaquin's unit rate, in miles per hour?
how do i set up this question using ratios? Fanny and Kevin shared a box of markers in the ratio 5:3; fanny gave half of her share to Kevin. Kevin then had 30 more markers than fanny. How many markers did fanny give to Kevin?
I do not understand where you got your formula: K+(1/2*F) - 1/2*F=30
Now K+(1/2*F) - 1/2*F=K. Please make it simpler.
this takes a lot of time you need to be patient i guess
Just don't let the equations sit there all lonely. It's hard to go straight up- you'll never convince a 2 on the bottom of 1/2 to climb over that roof. But diagnolly, any number can climb steps, even I can (and I weigh 220 lol). So Bring the lonely numbers from the bottom, to the tops diagnoly across, through the '=' elevator. Just make sure you do it to both numbers, or you end up with a very angry left out number, that will snitch on your teacher to get you marked wrong on the test!
The height of a building is 3 3/8 in. on a scale drawing. Find the actual height of the building if the scale used is 1 in. : 4 ft.
3 3/8 = 27/8, 4 ft = 48 in.
27/8 : x = 1 : 48
x = 162 in. = 13.5 ft.
The building is 13 and a half feet tall.
How come at 7:48 its < 1/5 yr cell phone?
How did he find the answer 6:40?
How do I find 2/5 pound of mixed nuts for 2.50
In 5:32, why is the height of Ben Nevis left as 67 times 20?
I get it but I don't. For example if I have 6/x=9/5 if I cross multiply I get it right every time but the problem is I can't cross multiply when I have x+3/1-=11/5. So my problem starts at the very beginning because on the first set if I don't multiply and instead I chose to solve for X first I don't get the right answer like this: 6/x . x= 9/5 . x ok so that cancels out the x and leaves me with 6=9/5 . x, then I multiply both sides of the equation by 9/5 to get rid of this part and I end up with 6=54/5 which is not the same from the cross multiplication which is 30/9. Why do I sometimes get this problem and some times I don't when I do the exact same steps every time? Now I did noticed that Sal sometimes flips the fraction, but How do I know when to do that, how do I know which term I should cancel out first in order to get the correct answer every time?
I believe you are solving for x incorrectly

6/x = 9/5. Multiply both sides by x
(6/x)*x = (9/5)*x
6 = 9x/5 Multiply both sides by 5
6*5 = (9x/5)*5
30 = 9x and divide by 9 to isolate x.
30/9 = 9/x
10/3 = x

When you have 9x/5 (or as you wrote it, 9/5 . x) you can't cancel it out by multiplying by 9/5. You have to multiply by the reciprocal/inverse, 5/9, which is what happened in the solution above (except in more steps). Just to show you

6 * (5/9) = (9/5 . x) * (5/9)
30/9 = x
10/3 = x
What Would E And N Stand For ? A Number ?
there different then other ratios
you need to be advanced for this kind of math
A family has a total after tax income of $2400/month and a monthly mortgage expense of $800. find the ratio of mortgage expense to after tax income?
is it 80:240 the answer
If the total cost of x apples is b cents, what is a general formula for the cost, in cents,
of y apples?
what does ratio have to do with proportion? Sorry if it seems like a stupid question i just don't know.
A ratio shows the how the proportion works. A ratio such as 8:3 says that for every 8 of the first item, you will always have 3 of the other. In other words, say were were talking about weight: "These 8 oranges have the same weight as 3 of these big potatoes, so their weights are proportional to each other at a ratio of 8 to 3."
whats agrivating me is why do you need to multiply anything times x? @00:29 whats the point?
How do I find an actual ratio?
If 12/8 = x/9 why does it not follow that 3/2 = x/9 in that same equation? Why does simplifying 12/8 as a ratio (and a fraction) not work in that equation?
At 4:20, why does Sal divide 4800 by 48? He's supposed to be cross-multiplying, but he divides like this for all three problems and then multiplies what's left over Why?
maybe because he didn't notice or something like that.
how do you answer this? : 7x = 9y
Thanks! :D
this is a great way to learn how to set up porportions
Yeah its kindof like microsoft paint. if you look close he has like a little kite connected by tiny dots.
what is ratio what is proportion what is the difference
a ratio is, for example 4:9 but a proportion is 4:9=x:18 usually it is solve for x
My parents bought a house in Austin for 2 million dollars. The total, which was 3 million and 32 dollars, was some(x) amount of money with 5% tax. How much is the 'some amount of money'?And they bought a riverboat for 1/341 of the some amount of money. How much is the riverboat?
Help me Sal, I really need alot of help on my preparation for CCAT testing.

A hare and a jackal are running a race.Three leaps of the hare are equal to four leaps of the jackal. For every six leaps of the hare,the jackal takes 5 leaps.Find the ratio of their speeds.
A. 64:25
B.8:5
C.5:8
D.25:64

I don't understand how the choices even relate to the question. Please help
At 7:45 and 8:43 I don't understand what he means by 1/5 year. Why isn't it just one year?
Well, he's just saying that it is 1/5 year, which is 2.4 months. Its just the problem.
Why is fractions different from proportions.
How would you solve the equation: 4:n:5=5:8:m? How would I find the value of the two variables?
You'd need to do it one piece at a time. Start with 4/n = 5/8, then do 4/5=5/m.
What is the easy way to find out the answer
How do you solve a ratio proportion with slope
could u specify the question?
I don't understand which to multiply by: x or the number below/above x?
Someone please explain simpeler, im only a 6 grader!
all of the the video the guy goes to fast
Sylvia,
Use the pause button when you want him to stop so you can think about what he said.
And just click along the time stripe to go back a little if you want him to repeat something.
You have control at Khan Academy.
In problem #2, why the hell does it say Proportion ? It made me look in the wrong place because I thought they wanted me to create a PROPORTION ! And what Sal does aren't proportions,,, Am I right or wrong ? Thanks
Can you simplfiy the proportions before you cross Multiply ?
Yes, but only if both sides can be simplified.
how do you cross-multiply?
To cross multiply you simplify the vertical fraction ex: 6/8=3/4 and the say the problem is 3/4=x/2 you do 3*2=4x and then 6=4x and then divide both sides by four, (to cancel the four on the right) and you get 1.5
AR 735 why dud he put y in fir 1/6
Hi, at around 9:41, Sal puts the number of students that have a cell phone that is more than 1 year old (the 7/15 x) over the number of people that have cell phones (2/3 x). Can someone give me a bit of intuition about why this makes sense? Thanks in advance.
How do you solve the problem at 2:47. I still don't understand how to solve these kind of problems.
in half an hour the bucket is 1/5 of the way full. What is the rate at which the water is leaking?
In the second problem, the one of the cell phones, you subtract the quantity of students who have a new cell phone out of the students who have a cell phone.
Why do you do another step, if that was what the problem wanted to know?
Report a mistake in the video
Example:

At 2:33, Sal said "single bonds" but meant "covalent bonds."

Report a mistake in the video


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