Question

How can I turn word problems into algebra equations? Can you put in kid words too? :}

Answer 1

Anyoneee?

Answer 2

Assign to each unknown a variable to represent it
Take the sentence and reduce the relationships to less complex language
continue and continue to reduce the number of words until you're left with just the variables you've defined
you should end up with just variables, some equal signs and operators (+,-,/,*)

Answer 3

???

Answer 4

do you have a specific example?

Answer 5

...no

Answer 6

would you like me to make one up?

Answer 7

sure

Answer 8

ok
together our ages total to 62
i am 12 years older than you are. how old am i?

Answer 9

50

Answer 10

it's wrong

Answer 11

so this is what we do

Answer 12

first introduce a variable, you can pick any letter. then write down precisely what it means. make sure you know it is going to be a number. i will use
"m"

Answer 13

and say that
"m is my age"

Answer 14

ok

Answer 15

then i will see if i can find some other expression involving only m.
for example, if i am 40 then you must be 30 (because i am ten years older) and if i am 35 you must be 25 for the same reason

Answer 16

so if my age is "m" then your age must be
\[m-10\]

Answer 17

yea

Answer 18

so now i have both our ages written as variables. mine is
\[m\] and yours is
\[m-10\]

Answer 19

ok

Answer 20

sage = 12 + you, sat said his age is 12 more than yours
you + sage = 62, he said that your age and his combined to 62
you = ?, what is your age?
you = 62 - sage, your age from the 2nd equation above is this
= 62 - (12 + you), substitute sage's age in equation 1 here to have only on variable, "you"
you + you = 62 - 12, now solve by arranging terms
2you = 50, solve some more

you = 50/2, arithmetic, easy
= 25

That's it, turn language into variables into equations.

Answer 21

finally i find another expression for our ages. i know that the total of our ages is 62, so i write that down as well

Answer 22

ok

Answer 23

my age plus your age is 62
\[m+m-10=62\]

Answer 24

now i have some algebra that i can solve with no words attached

Answer 25

wait where did the second m come from

Answer 26

lets go slow

Answer 27

my age is
\[m\] and your age is
\[m-10\] right?

Answer 28

yea i understand now

Answer 29

so when i add them together i get
\[m+m-10=62\] which says my age plus your age is 62

Answer 30

well i mean i understand where you got the m from

Answer 31

ok

Answer 32

if parentheses help i could put
\[(m)+(m-10)=62\] but they are unnecessary

Answer 33

yea

Answer 34

now it is customary to write
\[2m\] instead of
\[m+m\]so we could rewrite this as
\[2m-10=62\]

Answer 35

ok

Answer 36

to solve now takes two steps. add ten to both sides
\[2m-10+10=62+10\]
\[2m=72\]

Answer 37

why do you need to add 10?

Answer 38

then to find m divide both sides by two or just think "twice my numbers is 72, so my number must be half of 72 and half of 72 is 36

Answer 39

why did i add 10?

Answer 40

i have an equation that is
\[2m-10=62\] and i am trying to find the number m

Answer 41

yea

Answer 42

in other words my job is to get
\[m=\text{something}\]

Answer 43

so you're trying to get rid of the 10?

Answer 44

exactly. i want m all alone, so i have to get rid of the ten first

Answer 45

think of it this way. i have
\[2m-10=62\] and i say "what was this before i subtracted 10?" well it must have been 72 first right? i know this because
\[62+10=72\]so i write
\[2m-10=62\]
\[2m=72\]

Answer 46

ok

Answer 47

then i know that two times my number is 72, so my number must be half of 72 and half of 72 is 36

Answer 48

but if you subtracted 10, wouldn't it be
\[2m = 62\]

Answer 49

hold on
we started with
\[2m-10=62\] right?

Answer 50

yea

Answer 51

so is it clear that if
\[2m-10=62\] then
\[2m=72\]?

Answer 52

...not really

Answer 53

in other words i have a quantity 2m
when i subtract ten from it i get 62
that means the quantity itself must be 72

Answer 54

lets think like this. i have some money in my pocket. i spend 10 dollars and am left with $62
who much money did i start with?

Answer 55

ohhh ok u started with $72

Answer 56

right. like saying
\[\text{my wallet} - 10 = 62\]

Answer 57

so i had $72 in my wallet to begin with

Answer 58

and you know this because you added 10 to 62 to get 72

Answer 59

yea

Answer 60

in our algebra problem we have
\[2m-10=62\] so we know that
\[2m=72\]

Answer 61

and if twice my age is 72
then my age must be 36

Answer 62

yea

Answer 63

in math we would say "divide both sides by 2" but it is really just common sense. two times my age is 72, my age is half of 72 which is 36

Answer 64

yea

Answer 65

so now you know my age. my age is 36
and we also know your age. you are ten years younger than i am so you must be 26

Answer 66

ok

Answer 67

and you see that we have solved it because the total of our ages is
\[36+26=62\] and the numbers are ten apart

Answer 68

yep

Answer 69

if you have a specific problem like this feel free to post it and you will get lots of answers

Answer 70

thank you soooooooooooooo much satellite