# Solving Word Problems in Algebra : – 4 Videos-in-1 Lesson dealing with Translation of Expressions welcome to another video from UltimateAlgebra.com in this video we will be introducing ourselves to word problems
specifically we will familiarize ourselves with the implication of
different words and expressions .Being able to translate the various
expressions to math forms 90% of the requirement to be good in solving word
problems. Let’s look at the most common expression used. Addition expression – the
following expression implies addition one increase by two more than three
added two for some five comparative words that denote more than longer
faster taller and so on if we have five increase by three this is the same as 5
plus 3 if we have 2 more than 8 this is the same as 8 plus 2 R 2 plus 8 you can
interchange numbers in addition subtraction expressions the following
expressions implies subtraction one decrease by two less than three taken
from 4 subtract it from 5 difference 6 comparative words that denote less then
smaller shorter slower and so on one important thing to know about
subtraction expressions is the order matters if we have 8 decreased by 5 this
is 8 minus 5 this is straightforward but if you have less then the second number
is written first or we can say is written backwards so 8 less than 5 is 5
minus 8 notice we had the 5 first we say that for addition order doesn’t matter
for subtraction if you have less then subtract it from taken from are any of
the comparative words that denote less then we write the second number first he
is two years younger than X this will be X minus 2 notice we wrote the X first
and the two second multiplication expressions the following implies
multiplication 1 multiplied by 2 times three twice thrice double triple
and so on for product so if we have to multiply by X that will be two times X
which is simply 2x division expressions the following implies division 1 divided
by 2 quotient 3 shared equally 4 / if we have 20 shared equally among 4 boys this
will mean 20 divided by 4 next we look at expressions that implies equal to 1
is 2 was three gifts four becomes five equals so if we have two plus three is
five it’s the same as this the is meant equal to finally to solve most word
problems you have to identify your unknown value and represent the unknown
value by x or any letter you prefer example if we say number minus four
we do not know that number so we can represent it by X so we have X minus
video you have to be familiar with these expressions in the next video we’ll be
looking at tons of examples have a great day goodbye. Welcome to another video
from UltimateAlgebra.com we are still looking at expressions and word problems
we’ll be looking at some examples. hope you have printed out the expression
sheet . You have to know all of it translate the following expression
number one to increase by four we know that increased by means addition so this
will be two plus four number two twice a number is four we see three keywords we
know that twice means multiplication exactly two times we know that a number
is our unknown so we can represent it by x
finally we have is which we know means equal to we can write this as 2 times x
equals 4 2 times X is the same as 2x so we have 2x equals 4 number 3 7 more then
3 times a number was 20 we have 7 more than means additions so we have plus a
number is our unknown we can represent it by X so 3 times a number will be 3
multiplied by X which is 3x finally we have was which means equals so we have
equals 20 our unknown doesn’t always have to be
represented by a number example 3 times Rachel’s age is 5 here the unknown is
Rachel’s age so we can represent it by X this will be 3 x equals 5 if we have \$10
subtracted from joel’s money becomes \$30 here we have becomes we know that means
equals so we have equals 30 next joel’s money is our unknown so we represented
by X remember we learned in the previous video that when you have subtracted from
you will write the second thing first so 10 subtracted from joel’s money is X
minus 10 important use of parentheses before we end this video we want to look
carefully at this for keywords sum difference product and quotient we
means multiplication and quotient means division but these terms denote a group
and it is necessary to put them in parenthesis then work from there
example the sum of 2 and X is 12 so here we can write it this way notice that end
is what is between the two numbers that we are adding let’s look at these two
statements 4 times 3 plus 5 and 4 times the sum of 3 & 5 we
notice that in both cases we have two operations we have times which means
multiplication we have plus for the first statement and some for the second
statement both meaning addition these statements does not mean the same thing
and will or yield the same results the first one is straightforward four times
three plus five from our order of operations we do our multiplication
first then our addition we multiply the 4 and the 3 to get 12 then we add the 5
to get 17 let’s look at the second one again we have 4 times but here we have
the sum of 3 & 5 we said we put this in parentheses so we have this from our
order of operations we know that we have to do parentheses first so here we will
add the 3 and 5 to get 8 then we will multiply 4 by 8 this will give us 32 if
we had not put it in parentheses we would have solved it as 4 times 3 plus 5
and we would have had it wrong I hope this example helps you understand why we
are making a big deal out of using parentheses for some difference product
and quotient we will end this video here please go over this video and try your
hands on as many examples as you can there will be no reason to continue to
the next lesson if you haven’t mastered this one have a great day goodbye welcome to another video from ultimate
algebra comm in the previous lessons we learned how to translate algebraic
expressions in this video we will use that to solve actual word problems let’s
take our first example Leslie’s age is 3 years more than twice Victor’s age if
the sum of their ages is 48 what will Leslie’s age and Victor’s age
be the first thing I like to do when solving any word problem of this nature
is to identify my subject or thing the question is about and represent them
with letters here we are looking at Leslie’s age and Victor’s age we can
represent Leslie’s age by L and represent Victor’s age by V now
let’s go sentence by sentence and translate the word problem into math
Leslie’s age which we represent by L is we know that is means equals three years
more than we know more than means addition twice Victor’s age means two
times Victor’s age we represented Victor’s age with V so this can be
written s to V next we are told that the sum of their ages is 48 we know that sum
is addition we are adding their ages so we have L plus V is 48 which is the same
as equals 48 now we’ve been able to set up the word problem we are going to use
substitution to solve it I will label this equation 1 and label this equation
2 since L is 3 plus 2v we can substitute the L in equation 2 with 3 plus 2b we
have 3 plus 2v plus V equals 48 we solve for V we have 3 V equals 48 minus 3 V
equals 15 so here we have victors H as 15 years but the question wants us to
find Leslie’s age also to find Leslie’s age we can substitute V equals 15 in
equation 1 we have l equals 3 plus 2 times 15 we solve for L to get 33
Leslie’s age is therefore 33 we can see that there are two things needed to
solve this question and you have to be a master in both one you should be able to
translate the word problem to you should be able to solve the equation in this
case the simultaneous equation we will end this video and look at more examples
in subsequent videos have a great day goodbye welcome to another video from
ultimate algebra comm we are still looking at word problems here we want to
look at implied meaning you are not always going to get all word problems
having a direct translation to math less solving
example to explain it a farmer sold a horse in a cow for \$210 he sold the
horse for four times the price of the cow how much did he get for each again I
start by identifying the things the question is about it’s about the price
of a horse and the price of a cow I will represent the price of the cow by sea
and represent the price of the horse by H now let’s read the question and
translate it a former sold a horse in a cow for 210
dollars this statement does not follow any of the things we learned about the
direct translations we can however notice that this means the price of the
horse plus the price of the cow equals 210 we call this our equation one he
sold the horse for four times the price of the cow here again apart from the
four times nothing follows the direct translation
we’ve been learning but we can see that this statement has the same meaning as
the price of the horse is four times the price of the cow so we can say that H
equals four see this will be our equation 2 so we are done with our
setting up next we want to use substitution to solve the equation we
can replace the H and equation 1 by 4 C now we have 4 C plus C equals 210 we
solve for C we have 5 C equals 210 C is therefore 42 next we can substitute 42
for C into the equation 1 or 2 and solve for H I choose equation 2 we have h
equals 4 times 42 we multiply to get H equals 168 so – farmer sold the horse
for 168 dollars and the cow for 42 dollars to be able to solve this
question you need to understand the implied meaning and translate it to
mathematics then as usual solve the resulting equation in this case
simultaneous equation we will end this video here have a great day goodbye

1. If you have a comment or question, post it here and we will answer it.
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2. Thanks

3. 10:08 ahhh, wait, what ??????? 3+2v+v=48,,,,,,, why would this not be 5v squared ??????? you just threw the + 2 and one of the v's away like their not there,,,,,,,
Also, how do you get Leslie's age of 33, cause 3+2=5 by 15=75 doesn't it ???????

4. She is beautiful!

5. Helped me, but I will still hate math my whole life

6. I love this algebra ohh this is my favorite

7. ive noticed that the mic kinda lowers and then becomes louder

8. Words cannot describe how much I hate maths, especially word problems 😑

9. interesting!!

10. Good job but you are too first, some of us are slow learner

11. I want to ask you one question of solving word problems

12. Thank's for sharing mam!

13. Would be gréât another video with more complicated ones

14. marc has 45 cd and andrea has 61
marc buys 4 new cds and andrea buys 2 new cd each months
how many months will Andrea and March have the same number of cds?

15. four fifths of anumber are more than three fourths of a number by 4. find the number.

16. Question= a comic costs 23 pence more than a book. If four books and five comisc cost 3.22, then what is the price of a @ultimatealgebra

17. You Forgot The "Gozinto" In the Division Jargon, Like 5 Gozinto 10= 2 times. It's very important!

18. Thank you, but narrator's voice was not easy for me to follow

19. Hello, can someone please explain to me how 3v = 48 – 3? 10:00 Why are we subtracting the 3? I understand how the 2nd equation is operated but not this first one. I'm really lost on how this first one is being solved and how Victor's age became 15.

20. Can you mam make it clearer how did you come to 15 your answer in L + V (eq 2). I need to see them all step by step?

21. thank you so much… please more examples of word age problem

22. Does anyone know where the sheet im supposed to download is for each seperate video? lol cant find it

23. At 9:58 I don't understand how you got V =15. I'm not good at this at all.

24. Thank you

25. it would be nice to detail and explain the last part of equation rather then let us figure it out, like cancelling v's and divisions, it seems like towards the end, they do short cuts.. 🙁