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### Course: 7th grade > Unit 1

Lesson 5: Writing & solving proportions# Writing proportions example

Some examples of writing two ratios and setting them equal to each other to solve proportion word problems. Created by Sal Khan.

## Want to join the conversation?

- Would the answers be:

#1: $5.78

#2: 11.2 apples

#3: 6 eggs

I'm only asking because I'm not sure if I fully understand this unless I get the answer right...(207 votes)- and im pretty sure you wouldnt add 11.2 apples it would be 11.(14 votes)

- Lonnie was paid 115.50 for 14 hours of work. work At this rate,how much will Lonnie earn for working 22 hours? How do I set up the problem.(40 votes)
- (115.5/14)*22= $181.5

(sorry I just do it a very different way.)(8 votes)

- This equations make no sense, I have no idea on how to learn them, for example; here i have one;

5 erasers cost $9.85.

Which equation would help determine the cost of 9 erasers?

Normaly I will divide the price by 5 to determin the cost of one eraser and then multiply by 9 to determin the cost of 9, but here the system gives me this;

5/9=$9.85/x as a final equation that I should have done it ?

Can someone explain to me how this equation makes sense?(6 votes)- Same trouble here. I don't understand why the cost is the denominator.(4 votes)

- I got 8.96 for question one, 9 divided by 11.50 gives me 1.277 ( repeated sevens) rounded off gives 1.28, times 7 gave me 8.96. Is this incorrect?(4 votes)
- 9 divided by 11.5 does not = 1.2777...

Sounds like you actually did 11.5/9 which does = 1.2777..., which is ok.

Multiply that by 7 and you get the actual answer of 8.94

Your answer is a little off because you rounded too early. Keep 3-4 of the 7's rather than rounding when you did. 1.27777 * 7 = 8.94439, then round to 8.94

Your answer will be more accurate.(9 votes)

- I wonder why he doesn't solve it(7 votes)
- Because it's not in the lesson to solve it, at the very beginning, he even says, "What I want to do in this video is not solve the word problems, but just solve the equation."(1 vote)

- For the last one cant you just do 2 times 3(6 votes)
- For the ratios of the first problem, if you're confused to how he got 11.50/9 = x/7.

Well, we know 9 markers cost $11.50. Let's say we do an equation with a constant to find out how to get how much a certain number of markers cost.

So: $11.50 = k * 9. That k represents the cost of 1 marker. Makes sense, right? Because the cost of 1 marker times 9 markers is $11.50.

Now, you can solve for k by seeing that: $11.50/9 * 9 = $11.50.

So: k = 11.50/9.

Now, do the same for the seven markers. x = cost of 7 markers.

x = k*7. Solve for k? k = x/7. Note the k is constant and is equal to the k for nine markers. So if k = k, we can say 11.50/9 = x/7.

Now for 9/11.50 = 7/x, you just flip the variables around in the equations we wrote and it changes the meaning of k.

Btw, if you divide that 11.50/9 you get roughly $1.28 per marker or $1.277777 repeating forever for every marker. Since the k is the same ratio, you can plug that in for the equation of x, and multiply $1.28 x 7 to get $8.98, which is close to the cost of 7 markers: not quite since it's an estimate but it is good enough.

If you want to get the actual value you would multiply that 1.2777777778 by 7 to get 8.944444, which you can round to $8.94. I prefer just using $1.28 x 7 since it's only like 4 pennies off and it's easier to calculate.(6 votes) - i am very confused can you please make a video and simplify it(5 votes)
- It has a lot of variables and they use basic Algebra so it can be confusing if you don't know it.(1 vote)

- I'm still confused on how to solve the equation.(4 votes)
- So some questions are

#1 $5.78

#2 11.2 bananas

#3 6 apples(3 votes)

## Video transcript

I have three word problems here. And what I want to
do in this video is not solve the word problems
but just set up the equation that we could solve to get the
answer to the word problems. And essentially, we're
going to be setting up proportions in either case. So in this first problem, we
have 9 markers cost $11.50. And then they ask us, how
much would 7 markers cost? And let's just set x to
be equal to our answer. So x is equal to the
cost of 7 markers. So the way to solve
a problem like this is to set up two ratios and then
set them equal to each other. So you could say that the ratio
of 9 markers to the cost of 9 markers, so the ratio of
the number of markers, so 9, to the cost of the
9 markers, to 11.50, this should be equal to
the ratio of our new number of markers, 7, to whatever
the cost of the 7 markers are, to x. Let me do x in green. So this is a completely
valid proportion here. The ratio of 9 markers
to the cost of 9 markers is equal to 7 markers to
the cost of 7 markers. And then you could
solve this to figure out how much those 7
markers would cost. And you could flip
both sides of this, and it would still be a
completely valid ratio. You could have 11.50 to 9. The ratio between the cost
of the markers to the number of markers you're
buying, 11.50 to 9, is equal to the ratio of the
cost of 7 markers to the number of markers, which
is obviously 7. So all I would do is flip
both sides of this equation right here to get
this one over here. You could also think about
the ratios in other ways. You could say that the ratio
of 9 markers to 7 markers is going to be the same as
the ratio of their costs, is going to be equal to the
ratio of the cost of 9 markers to the cost of 7 markers. And then, obviously, you could
flip both of these sides. Let me do that in the
same magenta color. The ratio of 7
markers to 9 markers is the same thing as
the ratio of the cost of 7 markers to the
cost of 9 markers. So that is 11.50. So all of these would be valid
proportions, valid equations that describe what's
going on here. And then you would just have
to essentially solve for x. So let's do this
one right over here. 7 apples cost $5. How many apples can
I buy it with $8? So one again, we're going to
assume that what they're asking is how many apples--
let's call that x. x is what we want to solve for. So 7 apples costs $5. So we have the ratio between
the number of apples, 7, and the cost of
the apples, 5, is going to be equal to the
ratio between another number of apples, which is now x, and
the cost of that other number of apples. And it's going to be $8. And so notice here in this first
situation, what was unknown was the cost. So we kind of had
the number of apples to cost, the number
of apples to cost. Now in this example, the
unknown is the number of apples, so number of apples to cost,
number of apples to cost. And we could do all of the
different scenarios like this. You could also say the
ratio between 7 apples and x apples is
going to be the same as the ratio between
the cost of 7 apples and the cost of 8 apples. Obviously, you can
flip both sides of these in either
of these equations to get two more equations. And any of these would
be valid equations. Now let's do this last one. I'll use new colors here. A cake recipe for 5
people requires 2 eggs. So we want to know how many
eggs-- so this we'll call x. And you don't always
have to call it x. You could call it e for eggs. Well, e isn't a good
idea, because e represents another number once you
get to higher mathematics. But you could call them y
or z or any variable-- a, b, or c, anything. How many eggs do we need
for a 15-person cake? So you could say the ratio of
people to eggs is constant. So if we have 5 people for
2 eggs, then for 15 people, we are going to need x eggs. This ratio is going
to be constant. 5/2 is equal to 15/x. Or you could flip
both sides of this. Or you could say the
ratio between 5 and 15 is going to be equal to the
ratio between the number of eggs for 5 people-- let me
do that in that blue color-- and the number of
eggs for 15 people. And obviously, you could flip
both sides of this equation. So all of these,
we've essentially set up the proportions
that describe each of these problems. And then you can
go later and solve for x to actually
get the answer.