anonymous
  • anonymous
the greater of the numbers is 3 times the smaller. their sum is 44.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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sandra
  • sandra
ok here!
anonymous
  • anonymous
x-3*y x+y=44
sandra
  • sandra
ok so 1. x = 3*y 2. x + y = 44

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anonymous
  • anonymous
3*y+y=44
sandra
  • sandra
correct so far
sandra
  • sandra
ok so now what you want to realize, is that you can just combine all those y's
anonymous
  • anonymous
3*2y=44
sandra
  • sandra
ok right, so 3*y can also be written as 3y. basically in words this means "I have 3 ys"
sandra
  • sandra
so if I "have three oranges", and I add one orange
sandra
  • sandra
I have 4 oranges
anonymous
  • anonymous
how did u get 3 y's
sandra
  • sandra
same thing with unknown variables
sandra
  • sandra
3*y by definition means 3 multiplied by Y, or Y multiplied by 3
sandra
  • sandra
just like 3*2 means "I have three 2's"
sandra
  • sandra
3*2 = 6 because 2+2+2 = 6
anonymous
  • anonymous
ok i get the 6
sandra
  • sandra
so 3*y is also y+y+y
sandra
  • sandra
that's the very definition of multiplication
sandra
  • sandra
so shorthand, we write that as 3y
anonymous
  • anonymous
so it is 3*2y=44
anonymous
  • anonymous
6y=44?
sandra
  • sandra
and so 3y + y = (y+y+y) + y = 44
sandra
  • sandra
some examples: 3y+y = 4y 2x + 2x = 4x x+2x = 3x x + x = 2x
sandra
  • sandra
so in your example, we got to 3y+y = 44
sandra
  • sandra
and hence 4y = 44
sandra
  • sandra
so can you solve for y from there?
anonymous
  • anonymous
so we are not multiplying the 3*2y?
anonymous
  • anonymous
i thought x=3*y
sandra
  • sandra
because the 3 is referring to 3 times the first y
sandra
  • sandra
not the second
sandra
  • sandra
if it helps you visualize, use parentheses when you substitute
sandra
  • sandra
so we had x=3*y
anonymous
  • anonymous
ok. so 3*y=4y+y?
sandra
  • sandra
so when we substitute , we have (3*y) + y = 44
sandra
  • sandra
3*y is the same thing as 3y - just be convention people usually leave off the multiplication symbol
sandra
  • sandra
so we have (3y) + y = 44
sandra
  • sandra
and hence 4y=44
sandra
  • sandra
and now we need to divide both sides by 4, to get y alone
anonymous
  • anonymous
11
sandra
  • sandra
correct =)
sandra
  • sandra
so I'm going to ask you a few follow ups. what is 5y + 5y?
sandra
  • sandra
this is just for practice
anonymous
  • anonymous
i was confused bcuz i added the 2 ys that i saw and then tried to multiply
sandra
  • sandra
exactly
anonymous
  • anonymous
10y
sandra
  • sandra
great what is 5y + 1y
anonymous
  • anonymous
6y
sandra
  • sandra
and now what is 5*y + y
anonymous
  • anonymous
6y
sandra
  • sandra
exactly =) because multiplication is always first
sandra
  • sandra
what you were doing was 5 * (y+y) , essentially
sandra
  • sandra
but what you wanted was 5*y + y
sandra
  • sandra
so now you got it though =)
anonymous
  • anonymous
so for the one we just did 44,11?
sandra
  • sandra
well, if 11 is y, then what is X?
sandra
  • sandra
you need to substitute 11 for y in any of the first equations
anonymous
  • anonymous
33
sandra
  • sandra
correct
sandra
  • 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
  • sandra
this is really the foundation for a lot of higher level math.
anonymous
  • anonymous
ok. i hope i remeber this. do u have any tips to remember
sandra
  • 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
  • sandra
4. You can always combine like terms - i.e. 3y + y = 4y
sandra
  • sandra
and at the end, once you think you've solved the problem, you can ALWAYS check your work
sandra
  • sandra
so you just told me that the bigger number is 33, and the smaller number is 11
sandra
  • sandra
you can put both of those numbers back into your original equations, and see if the equations are true
sandra
  • sandra
if they are, then you were right!
sandra
  • sandra
if not, then you go back and see where you messed up a bit
sandra
  • sandra
but for these types of problems, you should never be asking yourself if you were right
sandra
  • sandra
you should be able to put your answers back into the equations, and see if they hold true
anonymous
  • anonymous
that will definitely help if i check my work
sandra
  • sandra
hey hip, I have to go for now! but keep trying, keep asking here, and I'll be back around.
sandra
  • sandra
I'm glad I could help a bit!. good luck, you'll get there for sure
anonymous
  • anonymous
you helped A LOT!! thank you so much
sandra
  • sandra
no problem! ttyl
anonymous
  • anonymous
bye

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