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so in this section we're going to bring together everything we've learned about
equations
into problem solving equation
so one of the first things that you should think about is you should
remember
those keywords that we talked about so for example
if i said something like
the quotient
of triple a number
and five
gives one
what i mean by that is well quotient means division
triple a number means three times x so
division between three times a number and five gives one so we should be able
to take
the words and translate them into an equation or an expression depending what
the sentence is
and with that being settled we're going to use that idea to solve problems and there
is a group of problem-solving steps so let me write them out
so whenever we have problems to solve we're going to follow the following steps
so step one is going to be to understand the problem
and the idea here is
that to understand the problem you may need to reread it
a couple of times you have to draw a picture out just to see if you have an
idea of what's being said
you may have to quickly just come up with a solution in your head to see
if that solution would make sense just to know what kind of problem you're
dealing with then you have to choose a variable to represent some sort of unknown
most problems have unknowns or at least one of them
so step two is we're then going to translate our problem
into an equation
this is important because once you translate into an equation
usually that'll get you to the answer translating a problem into an equation
is half the battle
but it makes things a lot easier to understand
step three is going to be to obviously solve the equation
and step four is going to be to interpret the
solutions so one of the things that we're doing is when we're solving
problems
we put in a variable for some unknown
that unknown may not be what the problem was asking so it's important for us to
interpret whatever answer we get to understand if that is the answer that
they're asking for
or if that's something
like an unknown we made up in order to get us to the answer
so all these are important and i would add
that step five though this is not part of your book is to check your
solution
so first of all track the solution to the equation to check if your
solution makes any sense
in the context of the problem
so
i've already written down a problem here for us to do so let me read it out
the problem says the distance from cincinnati ohio to denver colorado
it's seventy one miles less than the distance from denver to san francisco
if the total of the two distances is two thousand three hundred and ninty nine miles
find the distance from denver san francisco
so the first thing that would pop up in my head is wow this is a lot of stuff
that's being said there's a lot of city names
there's a lot of mileage so i don't actually know what's going on just by
looking at it
so this is where
understanding the component that comes in at step one we want to understand the problem
as much as possible
so you should read this as many times as you want pause the video if you want to
what i'm going to do is draw a picture because i like seeing things in pictures
so the idea is say that you have
the united states here
so rough picture of the united states but
so you have the U.S. here
so we're talking about three cities
we're talking about
cincinnati ohio which is right here
so this this cincinnati
we're talking about denver which is somewhere over here
and we're talking about san francisco
which would be here
so we have our three cities
and you don't have to know where they are on the map you can just kind of plot them
down
and we know couple of things we know
that
the last thing that they said
the total of these two distances is two thousand three hundred and eighty nine so they mean the distance
from cincinnati to denver
and then the distance from denver san francisco
so the total of the two differences is
two thousand three hundred eighty nine
we also know the difference from cincinnati to
denver isseventy one miles less than the distance from denver
to san francisco so i'm going to asign a variable i'm going to let the variable x
be the distance from denver
to san francisco
so if that's my x
i know that that the distance from cincinnati
to denver is seventy
one miles less than x less than the distance from
denver to san francisco
so from
cincinnati
to denver
is seventy one miles less than
the distance from
denver to san francisco so that's why it's x minus seventy one
finally i know that this is
the total of the to distances so altogether from cincinnati to san
francisco
that's going to be a total of
two thousand three hundred and ninety nine miles
so that's the total from cincinnati to san francisco if i go through denver
okay so all that being said now let's go ahead and
translate my problem into an equation
i know a few things i know the distance from
denver to san francisco i know the distance from cincinnati to denver that's
x minus seventy one
and i know that when i add these two distances together i get two thousand three hundred
ninety-nine so there's my equation there
x plus x
minus seventy one equals two thousand three hundred ninety nine
now let me solve my equation
i'm going to very much in the same way that i did before simplify the left side
of the equation
which means combine my like terms
and then use the addition property of equality
to add seventy one to both sides
so i get to 2x
equals two thousand four hundred and seventy
and finally use the multiplication property of equality
to divide both sides by two
i'm going to finish this up here on the right
when i do that i get x equals one thousand two hundred and thirty-five
miles
so what i need to ask myself is okay i have my x but i need to interpret my answer
so what was x well x if you remember was the distance from denver to san
francisco
that's exactly what they were asking us so i can just state that as my answer
they're not asking for the distance from cincinnati to denver but i can give you that as well
i can just take seventy one away from one thousand two hundred and thirty-five
that wil give me the distance from cincinnati to denver
so if i wanted to check if this makes any sense well it does make some sense logically
because it's only one thousand three hundred thirty five miles which is less than the
the distance from cincinnati to san francisco that makes some sense
i could also go ahead and plug it into my equation to check my answer
so let's try the other problem i put up
i'll read it out to you
so the other problem says
a woman's fifty seven thousand dollar estate is to be divided so
that her husband receives twice as much as her son
how much would each of them recieve
so step one is to understand the problem so go ahead and reread it as
many times as you need to
so that all those numbers make sense to you
and you know where everything stands
what i'm going to do is go ahead and asign some variables so
i know that her son will receive some amount of money and her husband will receive
twice as much as her son
so why don't i let
my unknown
be the son's portion of the estate
and the husband's portion is easy because
the husband's will be twice as much as the son
so if i just let that be to accept the husbands
and then i also know that the total for states
fifty seven thousand dollars
so whatever a husband gets was whatever sockets has to add up to sixty seven
thousand dollars so now let me jump over to that second support right equations
sobai equation is going to be the whatever her son gets
coz whatever a husband gets has to make up her entire state
there is no other way that this could grow because shes not given money to
anyone else on the socks on the way it's mentioned
and the problem
her son gets acts
her husband gets to acts
and the total is fifty seven thousand so that all of us i don't have any queries
you know we have to solve it
to solve this equation
we combine like terms except to excuse me three x
on the left
that we use the multiplication appropriately quality to the bible
substrate three
when we get acts equals fifty seven thousand delivered three you can do that
by that'll give you nineteen wasn't
did now here's what the trails lead part of the politics of the translate this
into a solution
they ask in the problem how much won't each of the d_c_ both the husband and
son
that came to say nineteen thousand consults access as well that sounds
kinda get
so the son get the facts which is nineteen thousand the husband
that's two acts
so whatever two times nineteen thousand which is which happens to be thirty
eight thousand
and that's why it's right there
so if you want to check this to at least you fingers up and make sure they add up
to fifty seven thousand that's a lot of stuff
level are possible
because i know this must be difficult to do it now
soap hungry disqualification as much as you walk past going to do is agreement
already so you could possibly if you need to
but i'm going to go ahead and just assign a terrible soap
by a variable x is going to stand for something that you have to set for the
price of the games
or the person the xbox
now
we know
that the xbox and the games cost five sixteen you know the xbox cost twice as
much as the games
into the game so i'm just gonna exp the price of the gate
and that the xbox
is three times as much as the games
so that's just going to be three acts
okay and that means that i also know that the total of the games
plus the xbox
is going to be five hundred and sixty dollars
so that i don't know if the spartans parked out there for for the probably
could have balked
if they take the call the cost of the games
plus the cost of the xbox
and going to get the total cost of the bible
so the kids cost explores the xbox costs three times that song was
and the total is five hundred sixty to one of the loss topic here
that'll be brought up to use them actually need to come by later sulfur
acts
neetu interpreter and so what is exiting publishes the xbox costs how much of the
games cost
due to the costs and the paddling and up to five sixty which should
so take that and do it on your own but that's not in a class at the end of the
questions