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