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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    ok here!

  2. anonymous
    • 5 years ago
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    x-3*y x+y=44

  3. anonymous
    • 5 years ago
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    ok so 1. x = 3*y 2. x + y = 44

  4. anonymous
    • 5 years ago
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    3*y+y=44

  5. anonymous
    • 5 years ago
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    correct so far

  6. anonymous
    • 5 years ago
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    ok so now what you want to realize, is that you can just combine all those y's

  7. anonymous
    • 5 years ago
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    3*2y=44

  8. anonymous
    • 5 years ago
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    ok right, so 3*y can also be written as 3y. basically in words this means "I have 3 ys"

  9. anonymous
    • 5 years ago
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    so if I "have three oranges", and I add one orange

  10. anonymous
    • 5 years ago
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    I have 4 oranges

  11. anonymous
    • 5 years ago
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    how did u get 3 y's

  12. anonymous
    • 5 years ago
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    same thing with unknown variables

  13. anonymous
    • 5 years ago
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    3*y by definition means 3 multiplied by Y, or Y multiplied by 3

  14. anonymous
    • 5 years ago
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    just like 3*2 means "I have three 2's"

  15. anonymous
    • 5 years ago
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    3*2 = 6 because 2+2+2 = 6

  16. anonymous
    • 5 years ago
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    ok i get the 6

  17. anonymous
    • 5 years ago
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    so 3*y is also y+y+y

  18. anonymous
    • 5 years ago
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    that's the very definition of multiplication

  19. anonymous
    • 5 years ago
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    so shorthand, we write that as 3y

  20. anonymous
    • 5 years ago
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    so it is 3*2y=44

  21. anonymous
    • 5 years ago
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    6y=44?

  22. anonymous
    • 5 years ago
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    and so 3y + y = (y+y+y) + y = 44

  23. anonymous
    • 5 years ago
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    some examples: 3y+y = 4y 2x + 2x = 4x x+2x = 3x x + x = 2x

  24. anonymous
    • 5 years ago
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    so in your example, we got to 3y+y = 44

  25. anonymous
    • 5 years ago
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    and hence 4y = 44

  26. anonymous
    • 5 years ago
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    so can you solve for y from there?

  27. anonymous
    • 5 years ago
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    so we are not multiplying the 3*2y?

  28. anonymous
    • 5 years ago
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    i thought x=3*y

  29. anonymous
    • 5 years ago
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    because the 3 is referring to 3 times the first y

  30. anonymous
    • 5 years ago
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    not the second

  31. anonymous
    • 5 years ago
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    if it helps you visualize, use parentheses when you substitute

  32. anonymous
    • 5 years ago
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    so we had x=3*y

  33. anonymous
    • 5 years ago
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    ok. so 3*y=4y+y?

  34. anonymous
    • 5 years ago
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    so when we substitute , we have (3*y) + y = 44

  35. anonymous
    • 5 years ago
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    3*y is the same thing as 3y - just be convention people usually leave off the multiplication symbol

  36. anonymous
    • 5 years ago
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    so we have (3y) + y = 44

  37. anonymous
    • 5 years ago
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    and hence 4y=44

  38. anonymous
    • 5 years ago
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    and now we need to divide both sides by 4, to get y alone

  39. anonymous
    • 5 years ago
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    11

  40. anonymous
    • 5 years ago
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    correct =)

  41. anonymous
    • 5 years ago
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    so I'm going to ask you a few follow ups. what is 5y + 5y?

  42. anonymous
    • 5 years ago
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    this is just for practice

  43. anonymous
    • 5 years ago
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    i was confused bcuz i added the 2 ys that i saw and then tried to multiply

  44. anonymous
    • 5 years ago
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    exactly

  45. anonymous
    • 5 years ago
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    10y

  46. anonymous
    • 5 years ago
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    great what is 5y + 1y

  47. anonymous
    • 5 years ago
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    6y

  48. anonymous
    • 5 years ago
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    and now what is 5*y + y

  49. anonymous
    • 5 years ago
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    6y

  50. anonymous
    • 5 years ago
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    exactly =) because multiplication is always first

  51. anonymous
    • 5 years ago
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    what you were doing was 5 * (y+y) , essentially

  52. anonymous
    • 5 years ago
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    but what you wanted was 5*y + y

  53. anonymous
    • 5 years ago
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    so now you got it though =)

  54. anonymous
    • 5 years ago
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    so for the one we just did 44,11?

  55. anonymous
    • 5 years ago
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    well, if 11 is y, then what is X?

  56. anonymous
    • 5 years ago
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    you need to substitute 11 for y in any of the first equations

  57. anonymous
    • 5 years ago
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    33

  58. anonymous
    • 5 years ago
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    correct

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

  60. anonymous
    • 5 years ago
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    this is really the foundation for a lot of higher level math.

  61. anonymous
    • 5 years ago
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    ok. i hope i remeber this. do u have any tips to remember

  62. anonymous
    • 5 years ago
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    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)

  63. anonymous
    • 5 years ago
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    4. You can always combine like terms - i.e. 3y + y = 4y

  64. anonymous
    • 5 years ago
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    and at the end, once you think you've solved the problem, you can ALWAYS check your work

  65. anonymous
    • 5 years ago
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    so you just told me that the bigger number is 33, and the smaller number is 11

  66. anonymous
    • 5 years ago
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    you can put both of those numbers back into your original equations, and see if the equations are true

  67. anonymous
    • 5 years ago
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    if they are, then you were right!

  68. anonymous
    • 5 years ago
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    if not, then you go back and see where you messed up a bit

  69. anonymous
    • 5 years ago
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    but for these types of problems, you should never be asking yourself if you were right

  70. anonymous
    • 5 years ago
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    you should be able to put your answers back into the equations, and see if they hold true

  71. anonymous
    • 5 years ago
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    that will definitely help if i check my work

  72. anonymous
    • 5 years ago
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    hey hip, I have to go for now! but keep trying, keep asking here, and I'll be back around.

  73. anonymous
    • 5 years ago
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    I'm glad I could help a bit!. good luck, you'll get there for sure

  74. anonymous
    • 5 years ago
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    you helped A LOT!! thank you so much

  75. anonymous
    • 5 years ago
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    no problem! ttyl

  76. anonymous
    • 5 years ago
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    bye

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