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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
How does this all work out
Proportions are direct comparisons between two numbers.
They are only expressed using fractions.
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!!
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).
at 5:31 the sun was awesome
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.
In problem 2 starting at 6:53 I still a little confused when divideing the different
varibles can someone please explain?
Thank You
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!!
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.
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.
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.
why did sal reverse the fraction 13/6 into 6/13 @ at the beginning??
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.
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?
x stands for the unknown in your equation. If we have the problem x/4=2/8, we have to solve to find x.
What does proportion mean again :D
it is all so confusing! Please Please explain it again.:D
smiles,
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!
why are we multiplying by nevis i understand nevis is same size but why multiply 2:55
plz answer
I dont get this at all it is to hard. =(
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.
HI SAL!! this video helped me understand ratios and propartins
I have a 4"x 6" photo, I would like to increase the size to 30" x ?" to maintain proper proportions. Thank you.
In 5:32, why is the height of Ben Nevis left as 67 times 20?
Isn't Mont Blanc spelled wrong? Isn't it supposed to be Mount Blanc?
"Mont" is the French word for "mountain". It just happens to look similar to the English word "mount" because French and English both developed much of their vocabulary from Latin. In English the name means "White Mountain", but we just tend to call it "Mont Blanc" regardless.
How do I find 2/5 pound of mixed nuts for 2.50
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=??
What if say the question is x-3/(over)5=7/3
then d cross multiply and find it out
Do you have worksheets which would help me with ratio and proportion
If you don't understand ratio and proportion, you should try the practice problems.
How do I find an actual ratio?
What is the technical definition of a proportion? #confused
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?
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 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
there different then other ratios
you need to be advanced for this kind of math
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.
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.
how would you cross multiply
a/b = c/d ---> a*d = b*c
At 09:09-9:23, did he just just cross multiply?
i think i may have missed a video......
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?
at 4:11 working backwards, can u work this out another way besides working backwards?? if so how would we?
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 did he say the answer for yukon is 4 less than 300 when i was 4 less than 600
why does it become 13/6X? what does it mean? can someone please explain?
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.
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.
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
I don't understand which to multiply by: x or the number below/above x?
These proportions are very hard
how do you answer this? : 7x = 9y
Thanks! :D
This is not really a question, more like a shoutouy-
Thanks for helping me pass my math and i might be able to move back up in my math class!!!
in 0:06 how did he get the five?
That is just part of the problem. He didnt solve anything anything to get it.
if u take 227/12 and 375/3 could make a proportion out of it?????
It wouldn't be an equal proportion, so nope.
how do u rewrite a quotient as s a ratio using the units in a denominator
The tallest moutain in Canada is not Mount Yukon, it is Mount Logan.
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
It takes Joaquin 1/5 hour to hike 1/4 mile. What is Joaquin's unit rate, in miles per hour?
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?
AR 735 why dud he put y in fir 1/6
how many killograms equals a gallon? i dont understand how to do this because one is volume and the other is mass
A gallon of water would have a different mass than a gallon of air or a gallon of mercury. You need to know the density to calculate kilograms per gallon.

But if the problem was "How many kilograms in a gallon of water", you can find a very close estimate.

A cubic centimeter of water has a mass of about 1 gram. A liter of water has a mass of about 1 kilogram. (Density of water varies with temperature, but 1 liter/1kg is a close approximation.)

So if the question was the mass of a gallon of water, you can use the following ratios to find your answer.
1 kg/1 liter
3.78541178 liters/ 1 gallon

I hope that helps
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 think that this question can only be solved using algebra.
Let's make F as the number of markers Fanny has, and K as the number of markers Kevin has.
F/K= 5/3
Now, it changes.
K+(1/2*F)-1/2*F=30
Now, K+(1/2*F)-1/2*F is just K.
K=30
It means, that the original number of markers Kevin has is 30. Let's test this out-
If Kevin had 30 markers, then Fanny had 50, and she gave him 25.
50-25=25, 30+25=55.
Kevin now has 30 more markers.

To answer your question- Fanny gave Kevin 25 markers.
Hope I helped you!
How do you solve the problem at 2:47. I still don't understand how to solve these kind of problems.
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
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
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.
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
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
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.
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! |:(
4,*,9,131/2 are in proportion then * is
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.
How come at 7:48 its < 1/5 yr cell phone?
How do I find the length of similar figure
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. : )
How pressure can be calculated if only height is given ?
Please help.
Thank you.
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!
Hi
trying to solve the problems in "proportion 1" I found myself stucked. I make an example

if I have 6/5 = x/7 I solve by doing (6/5 * 7/x) = (x/7 * 7/x)
Now let's have a look at this one
6/5 = 7/x. Assuming that the previous method is universal I should proceed in this way
(6/5 * x/7) = (7/x * x/7). The problem is that the system tells me "no man, this is wrong. You have to do (6/5 * x/1) = (7/x * x/1)".

It's fine for me. But I have this simple question: why? I really cannot understand it (I know I'm probably quite dumb).
does this pair of ratios form a proportion 3.5/1.2=7/8
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?!
cant i just use cross products to solve these problems. i mean thats what i am doing and it works.
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.
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?
I need some help solving this please?: 8/(x+3)=1/x +1
I still dont understand the mountain problem! Could someone help me?
I don't get the mountain question. How'd he get Ben Nevis's size?
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 ?
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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