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Mountain height word problem

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

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)

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
To answer your original question-
x= 7.9328..
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.
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!!
Not really a question but,
Thanks you Sal for being such a lifesaver! Now I understand math!
Yeah, I just found out today. XD
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.
at 5:31 the sun was awesome
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).
How does this all work out
Proportions are direct comparisons between two numbers.
They are only expressed using fractions.
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?
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)
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.
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.
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).
((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.
In problem 2 starting at 6:53 I still a little confused when divideing the different
varibles can someone please explain?
Thank You
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.
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!!
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.
What does proportion mean again :D
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
A sum of money is divided among A,B,C such that to each rupee A gets, Bgets 65 paisa and C gets 35 pais. If C's share is Rs.28 then the sum is:?
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.
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=??
I need to know how to set up this ratio problem to solve:
The ratio of the number of chickens to the number of ducks on farm was 3:8. There were 40 more ducks than chickens. When half the chickens and some of the ducks were sold, the ratio of the number of chickens to the number of ducks became 3:4. How many ducks were sold?
First you need to find how many ducks to chickens there were at first using the 3:8 ratio and the 40 more ducks information. Then you have to use the new ratio and solve for change in ducks.
How do I find 2/5 pound of mixed nuts for 2.50
I don't understand which to multiply by: x or the number below/above x?
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!
how do you answer this? : 7x = 9y
Thanks! :D
Someone please explain simpeler, im only a 6 grader!
I am really really really really really really really confused what do you mean?
How do I find an actual ratio?
I keep getting a different answer for the first problem and I'm not sure why.

E = 4800(44/48) = 4400
4400 = (220/67)N = (4400)(67) = 220N = 1340N
Y = 1340(289/67) = 1340(4.31343287) = 5780
Or worked out another way (1340/1)(289/67) = 387,260/67 = 5780.

Kahn's answer is 5960. What am I doing wrong.?
You flipped two digits around accidentally. The equation for Y is 298/67, but you wrote 289/67. : )
These proportions are very hard
How do you solve a ratio proportion with slope
could u specify the question?
what is the unknown number?
1/3 over 3/8, equals to 2/5 over the unknown number. what is the unknown number? how do i solve this problem/
(1/3)/(3/8)=(2/5)/(x) // *x, /(1/3), *(3/8)

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.
I must be color blind because I can not see the red marker on the black screen :(
How pressure can be calculated if only height is given ?
Please help.
Thank you.
why does it mention mount blane ate 3:32?
We are learning about this in class. I think it really helped, don't get me wrong! But it would be nice to have more examples...
whats the difference of a ratio and a proportion
Is this more complicated than it looks?
Bob building a house and garage. the house, garage and driveway and a colour bond fence on three sides, leaving the from of the block unfenced.
have quotes for turf @$7.20 per square metre and colour bond fence @$92 per linear meter. advised to order an extra 5%for both, to allow for joins, short lengths and damaged turf.
find the cost of landscaping the block?
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?
The ratio of men to women is 3:5 and the class contains 24 people. How many men will it take to make the ratio 1:1?
This one is really hard, especially with all the "big" fractions like 228/448, etc. Is there an easy way to tackle these problems? I am only starting to understand this! Aren't proportions just comparing numbers and/or fractions to each other?
yes, you can simplify these fractions. So 228/448 is equal to 57/112.
in half an hour the bucket is 1/5 of the way full. What is the rate at which the water is leaking?
how do you know whether to multiply all the numbers together to get the measurement of mt. yukon or not? how do you know thats the way to find out?
What Would E And N Stand For ? A Number ?
there different then other ratios
you need to be advanced for this kind of math
I have a 4"x 6" photo, I would like to increase the size to 30" x ?" to maintain proper proportions. Thank you.
in chemistry class, the girl to boy ratio is 9 to 3

if there are a totalof 60 students, how many girls are there?

from bai3006 the best gamer ever
does this pair of ratios form a proportion 3.5/1.2=7/8
why do you have to put an x
thank you Barry Desborough
What is the answer to this question,
A Honda is 22/93 the weight of a Toyota, and the Toyata weighs twenty-tons.
How many ounces does the Honda weigh?
T = weight of Toyota
H = weight of Honda

T = 20 tons
H = 22/93 * T --> H = 440/93 tons

440/93 tons * 32000 ounces/ton = 151,397.849 ounces
why multiply by N or B in the ratio what the concept what the actual rule

he said Y=289/67 N why
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.
How come at 7:48 its < 1/5 yr cell phone?
whats agrivating me is why do you need to multiply anything times x? @00:29 whats the point?
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.
4,*,9,131/2 are in proportion then * is
why are we multiplying by nevis i understand nevis is same size but why multiply 2:55
plz answer
what is the numbers for the mathamatical sequence pie
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.
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."
it is all so confusing! Please Please explain it again.:D
Brezy Angel Froehlich (that is all random letters up there)
A portion is when you give food out depending on who is there by the table. A Pro-portion is a professional version of that, where you give out numbers from one equation to the other equation, making sure to depend on the rules of math, you don't want one of your equation guests getting all 'undefined' on you!
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
how do u rewrite a quotient as s a ratio using the units in a denominator
HI SAL!! this video helped me understand ratios and propartins
Why 1/5 of a year?
He made an error. It is <1 year and > 1 year. As a teacher my mouth sometimes works faster than my brain. But his concept is correct.
What is the technical definition of a proportion? #confused
I don't get the mountain question. If Mont Blanc is 4800 meters high, than what is the size? It says mont elbert was 44/48 the SIZE of Mont Blanc. But what is the size? It doesn't tell me in the problem! |:(
I still dont understand the mountain problem! Could someone help me?
i dont get this. how does it work
help! i don't get this! HELP! :( !
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
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 to cater with problems involving triple ratios (x:y:z)?
So, would the fraction 1/5 equal to the ratio 1:5?
Tell you one thing... I don't like the new picts for the badges you have come up with. they don't look realistic and it looks as if you want it to attract small kids.... I like the old badges! Plzzz bring them back!
Sal solution seems complicated. I would have thought if you wanted to figure out what proportion of students of the ones that own cell phones have a cell phone that is older than a year would be 4/5 of 2/3 (1/5 have cell phone less than a year, so that means 4/5 have a cell phone greater than a year) However, this works out to a completely different answer than his. Can someone elaborate?
If 1/5 have new phones and 4/5 have old phones that means 5/5 students own phones, which is clearly wrong. The initial ratios are given in terms of the total student population (variable x in Sal's explanation). This is why some extra steps had to be taken to convert from total population to just those with phones.
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!!
cant i just use cross products to solve these problems. i mean thats what i am doing and it works.
x stands for the unknown in your equation. If we have the problem x/4=2/8, we have to solve to find x.
Can you simplfiy the proportions before you cross Multiply ?
Yes, but only if both sides can be simplified.
I don't get the mountain question. How'd he get Ben Nevis's size?
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?
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?
Report a mistake in the video

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

Report a mistake in the video

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