Writing Proportions

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.