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

- anonymous

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

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- sandra

ok here!

- anonymous

x-3*y
x+y=44

- sandra

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

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## More answers

- anonymous

3*y+y=44

- sandra

correct so far

- sandra

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

- anonymous

3*2y=44

- sandra

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

- sandra

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

- sandra

I have 4 oranges

- anonymous

how did u get 3 y's

- sandra

same thing with unknown variables

- sandra

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

- sandra

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

- sandra

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

- anonymous

ok i get the 6

- sandra

so 3*y is also y+y+y

- sandra

that's the very definition of multiplication

- sandra

so shorthand, we write that as 3y

- anonymous

so it is 3*2y=44

- anonymous

6y=44?

- sandra

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

- sandra

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

- sandra

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

- sandra

and hence 4y = 44

- sandra

so can you solve for y from there?

- anonymous

so we are not multiplying the 3*2y?

- anonymous

i thought x=3*y

- sandra

because the 3 is referring to 3 times the first y

- sandra

not the second

- sandra

if it helps you visualize, use parentheses when you substitute

- sandra

so we had x=3*y

- anonymous

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

- sandra

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

- sandra

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

- sandra

so we have (3y) + y = 44

- sandra

and hence 4y=44

- sandra

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

- anonymous

11

- sandra

correct =)

- sandra

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

- sandra

this is just for practice

- anonymous

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

- sandra

exactly

- anonymous

10y

- sandra

great what is 5y + 1y

- anonymous

6y

- sandra

and now what is 5*y + y

- anonymous

6y

- sandra

exactly =) because multiplication is always first

- sandra

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

- sandra

but what you wanted was 5*y + y

- sandra

so now you got it though =)

- anonymous

so for the one we just did 44,11?

- sandra

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

- sandra

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

- anonymous

33

- sandra

correct

- sandra

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

- sandra

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

- anonymous

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

- sandra

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)

- sandra

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

- sandra

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

- sandra

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

- sandra

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

- sandra

if they are, then you were right!

- sandra

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

- sandra

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

- sandra

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

- anonymous

that will definitely help if i check my work

- sandra

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

- sandra

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

- anonymous

you helped A LOT!! thank you so much

- sandra

no problem! ttyl

- anonymous

bye

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