Mountain height word problem
Mountain height word problem
- Let's start with a warm up ratio problem.
- Then we can tackle some harder word problems. So I have the
- ratio 13/6 is equal to 5/x.
- I don't like having this x in the denominator, so let's
- multiply both sides of this equation by x.
- So if I multiply both sides by x, what's going to happen?
- On the right hand side, this x cancels out with that x.
- And then the left hand side going to become 13 over 6x is
- equal to-- you're just going to have a 5 there.
- And then to solve for x, you just multiply both sides by
- the inverse of 13/6.
- These, obviously, cancel out.
- That's why I multiplied it by the inverse.
- And you get x is equal to 5 times 6, which is 30/13.
- Now one way that you might see this done-- it's kind of
- skipping a step-- is called cross multiplying.
- You look at a ratio like this, and you immediately say the
- numerator on this side times the denominator on that side
- is equal to the numerator on this side times the
- denominator on that side.
- Let me write that out.
- So you might sometimes see people immediately go to-- let
- me just rewrite the problem actually-- So that original
- problem was 13/6 is equal to 5/x.
- You might sometimes immediately see someone go to
- 13 times x is equal to 5 times 6.
- And it might look like magic.
- How does that work out?
- Why does that make sense?
- And really, all they're doing to get to this point is they
- are simultaneously multiplying both sides of the equation by
- both denominators.
- Let me show you what I mean.
- If I multiply both sides of this equation by 6 and an x,
- what's going to happen?
- If I multiply it by 6x times both sides of this equation--
- And where did I get the 6?
- From here.
- Where did I get the x?
- From there.
- Both denominators.
- What's going to happen?
- On this side of the equation, the 6 is going to cancel out
- with this denominator.
- And on the right hand side of the equation, the x is going
- to cancel with this denominator.
- So you're going to be left with 13 times x is
- equal to 5 times 6.
- So nothing fancy there.
- You're just multiplying by the denominators of both sides of
- the equation.
- And it looks like you're cross multiplying.
- 13x is equal to 5 times 6.
- And then from here, of course, you divide both sides by 13.
- You get x is equal to 30/13.
- Now that we're all warmed up, let's tackle some actual word
- So we have the highest mountain in
- Canada is Mount Yukon.
- It is 298/67 the size of then Ben Nevis.
- Let's Y for Yukon is equal to 298/67 the size of-- let's say
- N for Nevis.
- That's what this in green tells us.
- The highest peak in Scotland.
- Mount Elbert in Colorado is the highest peak
- in the Rocky Mountains.
- Mount Elbert-- so we have this other information here-- Mount
- Elbert is 220/67 the height of Ben Nevis.
- So let's say, E for Elbert.
- E is equal to 22/67 times Nevis.
- Times the same Ben Nevis, right there.
- And they're telling us more.
- And, it is 44/48 the size of Mont Blanc.
- So Elbert is equal to 44/48 the size of Mont Blanc.
- Let's write B for Mount Blanc.
- They also tell us Mont Blanc is 4,800 meters high.
- Mont Blanc is 4,800.
- meters high.
- So B is equal to 4,800.
- And they ask us, how high is Mount Yukon?
- So we have to figure out Y.
- So let's see if we can work backwards, and figure out all
- the variables in between.
- So let's start with this information here.
- B is equal to 4,800.
- E is equal to 44/48 times B.
- So E-- so Elbert-- is equal to 44/48 times Mont Blanc, which
- is 4,800 meters.
- Now if you divide that by 48-- 4,800 divided by 48 is 100.
- So Elbert is 44 times 100 meters high.
- So it's equal to 4,400 meters.
- Fair enough.
- Now we can use this information and
- substitute it over here.
- We get Elbert, which is 4,400 meters high, is equal to
- 220/67 times Ben Nevis.
- N for Nevis.
- To solve for Nevis, we multiply both sides by the
- inverse of this coefficient right here.
- So we multiply both sides by 67/220.
- So times 67/220.
- The 67 cancels with that 67.
- That 220 cancels with that 220.
- And then you get-- let's see, if I take 4,400 divided by
- 220-- 440 divided by 220 is 2.
- So this is going to be 20.
- So 4,400 divided by 220 is just 20.
- So you get Nevis is equal to-- I'll swap sides.
- So Ben Nevis is equal to 67 times 20 meters.
- And now that's what?
- 1,340 meters.
- Is that is right?
- Well, lets just leave it like that, because we could--
- actually it looks like that's 67-- I'm going to leave Nevis
- as 67 times 20 meters.
- And substitute it right there.
- So Yukon-- I'll just go down here, because I have more real
- estate there-- Yukon is equal to 298 over 67 times the
- height of Nevis.
- Nevis is 67 times 20.
- So times 67 times 20.
- Well I can divide 67 by 67, and I get Yukon is
- 298 times 20 meters.
- So Yukon is equal to 298 times 20.
- And what is that equal to?
- That is equal to-- Let's see that's 2 times 298
- is going to be 396.
- Oh sorry, it's going to be 596.
- This is almost 300, so it should be close to 600.
- This is 2 less than 300, so this should
- be 4 less than 300.
- And then, I have a 0 here.
- So it's going to be 5,960 meters.
- And we are done.
- Let's do one more of these word problems. All right.
- At a large high school, it is estimated that 2 out of every
- 3 students have a cell phone.
- And 1 in 5 of all students have a cellphone that is one
- year old or less.
- All right.
- So let's think about it.
- Let's say that x is equal to the total number of students.
- This first line, 2 out of 3 students have a cell phone, so
- we could say that 2/3 x have cell phone.
- That's what that green statement tells us.
- And then that purple statement-- 1 in 5 of all
- students have a cellphone that is one year old or less.
- So 1/5 x have less than 1/5 year cell phone.
- So they want to know, out of the students who own a cell
- phone-- so it's out of this-- that's our denominator.
- So let me write that down.
- That is our denominator.
- So out of the students who have a cellphone-- that's
- right there-- they want to know what proportion owns a
- phone that is more than one year old.
- So how many students have a cell phone that is more than
- one year old?
- Well, we could take the total number that have a cellphone,
- which is 2/3 x.
- 2/3 of all the students have a cell phone.
- We can subtract out all of the students that have a new
- cellphone-- a cell phone that is less than one year.
- Remember they're saying more than one year here.
- So we want to subtract out all the students with the new
- cellphone, minus 1/5x, and you will then have the proportion
- of students who have this right here.
- This is right here.
- This is, have greater than 1/5 year cell phone.
- They have a phone, but it's more than 1/5 years old.
- This is all of them that have a cellphone.
- We subtract out the new ones.
- So this is, essentially, all of the people who have an
- older than one-year old cell phone.
- So to solve this, we just subtract the fractions.
- So this is just going to be, let's see, 2/3 is the same
- thing as 10/15.
- That's 2/3 minus 1/5.
- The same thing as 3/15 x.
- Which is equal to 10 minus 3 is 7/15 x.
- Is the total proportion of students-- that's this
- orange-- what proportion owns a phone that is more
- than one year old?
- It's 7/15 x.
- That's an actual number.
- So if you want to know, out of the students who own a cell
- phone-- so out of the students who own a cell phone, right
- there-- 2/3x, what proportion owns a phone that it is more
- than one year old?
- This is the number that own a cellphone that is more than
- one year old.
- And this whole value is the proportion out of the students
- who have a cell phone.
- Lucky for us, the x's cancel out.
- And we are left with this is equal to 7/15 times the
- inverse of the denominator.
- You divide by 2/3.
- That's the same thing as multiplying by 3/2.
- And what does this equal to?
- Divide by 3.
- We are left with 7/10.
- So of the students who own a cell phone, 7 out of 10 of the
- students who own a cell phone, own a cell phone that is more
- than one year old.
- And we are done.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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Proportion: An equation stating that two ratios are equivalent.
:) (Hope this was Helpful!) (;
the way to test if the problem is = or in proportion is to cross multiply so 1/2 = 2/4 you multiply the numerator on the one side by the denominator on the other so 1 x 4 = 4 and 2 x 2 = 4 so since both numbers come to 4 they are in proportion. hope this helps.
A proportion is saying that two _ratios_ are the same. For example, 1/2 = 2/4 is a true proportion because if you multiply *both* the numorator and the denominator of 1/2 by 2, you get 2/4, which, when reduced, is 1/2. Hope this helps(:
*Ratio* : _The quotient of two quantities that are in the same unit_.
*Proportion* : _An equation stating that two ratios are equivalent_.
``` hope this helps
A Proportion is saying the ratio between L and M is the same as the ratio between C and W
3:9....................................................states that 3 and 9 have a relationship
9 : 27 ...................................................Same thing, 9 and 27 have a relationship
1:3::3:9::9::27..................................Says 1 and 3 have the same relationship as 3 and 9, also as 9 and 27. (A colon between them means you are stating them as a ratio. Two colon mean that you are setting them, (or that they are) related to each other in the same way.
Example of an Algebraic proportional problem
3:5::X:Y Set a new proportion where Y is 4.5 times what it is now.
Answer 3 :22.5::X:Y
Hope I didn't confuse you and helped.
(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)
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)
639= a*b*c (I just switched the letters, it makes it more convenient)
To answer your original question-
x*y*z equals your number (639).
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.
They are only expressed using fractions.
Thanks you Sal for being such a lifesaver! Now I understand math!
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?
3 art students for every 4 sci students
What all information can we get from that which is given?
1)The sum of their heights: 20 + 10 + 5 = 35m...and so on
2)The difference of heights: A - B = 20 - 10 = 10m(A is 10m taller than B)...and so on
3)The ratio of their heights: A:B = 20/10 = 2:1(A is 2 times the height of B)...and so on
4)A:B = 2:1 and B:C = 10:5 = 2:1(Notice A:B = B:C. When two ratios are equal it is called a proportion)
Is this the correct way to solve a problem like this?
65/1312 = x/100
1312x = 65(100)
6500 divided by 1312x
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
varibles can someone please explain?
I don't know whether to simplify the fractions and what should multiply fractions by (x).
((x) x 13/6 = 5/(x) x (x))
3/9 = y/21
examples: The ratio of students to teachers is 18 to 1.
The proportion of boys in the class is 6 out of 10.
I suppose more often proportion is used to compare something to the total, but mathematically they are the same.
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
Soy Joy Smoothie costs $2.75 and takes 2 oz. soy + 1 oz. vitamin supplement to make.
Vitaboost Smoothie costs $3.25 and takes 1 oz. soy + 3 oz. vitamin supplement to make.
Have 100 oz. each of soy & vitamins.
How many of each smoothie should store make to maximize profits?
using proportional reasoning.
Why do you do another step, if that was what the problem wanted to know?
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
Now K+(1/2*F) - 1/2*F=K. Please make it simpler.
Let's make F as the number of markers Fanny has, and K as the number of markers Kevin has.
Now, it changes.
Now, K+(1/2*F)-1/2*F is just K.
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.
Kevin now has 30 more markers.
To answer your question- Fanny gave Kevin 25 markers.
Hope I helped you!
if there are a totalof 60 students, how many girls are there?
from bai3006 the best gamer ever
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.
I don't understand how the choices even relate to the question. Please help
can someone put a question for me to solve in the comments?
Please help, I am in desperate need!
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).
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.?
of y apples?
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.
Brezy Angel Froehlich (that is all random letters up there)
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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...
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This is great, I finally understand quadratic functions!
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At 2:33, Sal said "single bonds" but meant "covalent bonds."
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