Question

the greater of the numbers is 3 times the smaller. their sum is 44.

Answer 1

ok here!

Answer 2

x-3*y
x+y=44

Answer 3

ok so
1. x = 3*y
2. x + y = 44

Answer 4

3*y+y=44

Answer 5

correct so far

Answer 6

ok so now what you want to realize, is that you can just combine all those y's

Answer 7

3*2y=44

Answer 8

ok right, so 3*y can also be written as 3y. basically in words this means "I have 3 ys"

Answer 9

so if I "have three oranges", and I add one orange

Answer 10

I have 4 oranges

Answer 11

how did u get 3 y's

Answer 12

same thing with unknown variables

Answer 13

3*y by definition means 3 multiplied by Y, or Y multiplied by 3

Answer 14

just like 3*2 means "I have three 2's"

Answer 15

3*2 = 6 because 2+2+2 = 6

Answer 16

ok i get the 6

Answer 17

so 3*y is also y+y+y

Answer 18

that's the very definition of multiplication

Answer 19

so shorthand, we write that as 3y

Answer 20

so it is 3*2y=44

Answer 21

6y=44?

Answer 22

and so 3y + y = (y+y+y) + y = 44

Answer 23

some examples: 3y+y = 4y
2x + 2x = 4x
x+2x = 3x
x + x = 2x

Answer 24

so in your example, we got to 3y+y = 44

Answer 25

and hence 4y = 44

Answer 26

so can you solve for y from there?

Answer 27

so we are not multiplying the 3*2y?

Answer 28

i thought x=3*y

Answer 29

because the 3 is referring to 3 times the first y

Answer 30

not the second

Answer 31

if it helps you visualize, use parentheses when you substitute

Answer 32

so we had x=3*y

Answer 33

ok. so 3*y=4y+y?

Answer 34

so when we substitute , we have (3*y) + y = 44

Answer 35

3*y is the same thing as 3y - just be convention people usually leave off the multiplication symbol

Answer 36

so we have (3y) + y = 44

Answer 37

and hence 4y=44

Answer 38

and now we need to divide both sides by 4, to get y alone

Answer 39

11

Answer 40

correct =)

Answer 41

so I'm going to ask you a few follow ups.
what is
5y + 5y?

Answer 42

this is just for practice

Answer 43

i was confused bcuz i added the 2 ys that i saw and then tried to multiply

Answer 44

exactly

Answer 45

10y

Answer 46

great what is 5y + 1y

Answer 47

6y

Answer 48

and now what is 5*y + y

Answer 49

6y

Answer 50

exactly =) because multiplication is always first

Answer 51

what you were doing was 5 * (y+y) , essentially

Answer 52

but what you wanted was 5*y + y

Answer 53

so now you got it though =)

Answer 54

so for the one we just did 44,11?

Answer 55

well, if 11 is y, then what is X?

Answer 56

you need to substitute 11 for y in any of the first equations

Answer 57

33

Answer 58

correct

Answer 59

good work =). I know the word problems can be frustrating, but believe me it's worth struggling through these until you have it down.

Answer 60

this is really the foundation for a lot of higher level math.

Answer 61

ok. i hope i remeber this. do u have any tips to remember

Answer 62

well, practice. and for these problems, three rules to remember:
1. Always try and turn the word problems into equations
2. You can perform the same operation on both sides of the equation and have both sides always still be equal
3. If you have two equations, and two unknown variables, you always just need to substitute one equation into the other (you can pick either variable)

Answer 63

4. You can always combine like terms - i.e. 3y + y = 4y

Answer 64

and at the end, once you think you've solved the problem, you can ALWAYS check your work

Answer 65

so you just told me that the bigger number is 33, and the smaller number is 11

Answer 66

you can put both of those numbers back into your original equations, and see if the equations are true

Answer 67

if they are, then you were right!

Answer 68

if not, then you go back and see where you messed up a bit

Answer 69

but for these types of problems, you should never be asking yourself if you were right

Answer 70

you should be able to put your answers back into the equations, and see if they hold true

Answer 71

that will definitely help if i check my work

Answer 72

hey hip, I have to go for now! but keep trying, keep asking here, and I'll be back around.

Answer 73

I'm glad I could help a bit!. good luck, you'll get there for sure

Answer 74

you helped A LOT!! thank you so much

Answer 75

no problem! ttyl

Answer 76

bye