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erica123 Group Title

one integer is 8 less than 4 times another integer. the product of the two integers is 60. What are the two integers? show work

  • 2 years ago
  • 2 years ago

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  1. slaaibak Group Title
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    Call the one integer x. call the other one y x = 4y - 8 xy = 60 Solve this.

    • 2 years ago
  2. erica123 Group Title
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    can you help solve it?

    • 2 years ago
  3. slaaibak Group Title
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    Substitute the x=4y-8 into the second equation

    • 2 years ago
  4. slaaibak Group Title
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    you will get (4y -8)y = 60 solve for y. then solve for x

    • 2 years ago
  5. SmoothMath Group Title
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    Here's the process, my little sugarplum: Pick your favorite equation and your favorite variable in that equation. Solve for that variable. Now, use that to substitute into the OTHER equation. This will give you an equation with just one variable in it =) Solve for that variable, and you should just get a number. Now, you know one variable, so you can look back at either of the first equations and use that variable to solve for the other one.

    • 2 years ago
  6. erica123 Group Title
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    i got y=-15 and x=-68?

    • 2 years ago
  7. erica123 Group Title
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    im not positive that thats correct

    • 2 years ago
  8. SmoothMath Group Title
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    no =( I don't think so.

    • 2 years ago
  9. slaaibak Group Title
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    Try again.

    • 2 years ago
  10. erica123 Group Title
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    i dont know what i did wrong :/

    • 2 years ago
  11. SmoothMath Group Title
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    Show me your work, okay?

    • 2 years ago
  12. erica123 Group Title
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    ok 60=(4y-8)y 60=4y-8y 60/-4 = -4y/-4 y=-15

    • 2 years ago
  13. slaaibak Group Title
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    The problem lies in line 2

    • 2 years ago
  14. erica123 Group Title
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    x= 4(-15)-8 x= -60-8 x=-68

    • 2 years ago
  15. erica123 Group Title
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    what the problem? :o

    • 2 years ago
  16. SmoothMath Group Title
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    (4y-8)y = 4y^2 -8y

    • 2 years ago
  17. SmoothMath Group Title
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    distribute, sweet thang.

    • 2 years ago
  18. erica123 Group Title
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    whoops! forgot the to square it. but then there are no like terms to combine how would we solve 60= 4y^2-8y

    • 2 years ago
  19. SmoothMath Group Title
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    Well, that's a whole 'nother kind of problem, and I'm guessing you've actually had a lot of practice with it, but it can be tricky, I understand. The most common ways are factoring or quadratic formula. Sound familiar?

    • 2 years ago
  20. erica123 Group Title
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    yes we have to move the 60 over so it becomes a zero so then we have the values a b c for quadratic equation

    • 2 years ago
  21. SmoothMath Group Title
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    Good =) And actually, if you want to try factoring, it works nicely for this one. But I'm a fan of the quad formula, since it always works.

    • 2 years ago
  22. SmoothMath Group Title
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    Yes =) Take out a common factor of 4 first though.

    • 2 years ago
  23. erica123 Group Title
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    2 and 2

    • 2 years ago
  24. SmoothMath Group Title
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    It makes it a lot easier.

    • 2 years ago
  25. SmoothMath Group Title
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    Nooo show me your factoring, please.

    • 2 years ago
  26. erica123 Group Title
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    4? isnt is 2 and 2 or 4 and 1?

    • 2 years ago
  27. SmoothMath Group Title
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    noope. show me your factoring.

    • 2 years ago
  28. SmoothMath Group Title
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    from 4y^2 -8y-60 = 0

    • 2 years ago
  29. erica123 Group Title
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    4y*y ?

    • 2 years ago
  30. SmoothMath Group Title
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    ... okay you aren't good at factoring. That's okay. A lot of people aren't. Use the quadratic formula.

    • 2 years ago
  31. erica123 Group Title
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    ok

    • 2 years ago
  32. SmoothMath Group Title
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    I only say that because it's a whole different issue. We can work on it another time =)

    • 2 years ago
  33. erica123 Group Title
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    ok after i do the quadratic equation i will get 2 different answers and those will be the answer to the problem right?

    • 2 years ago
  34. SmoothMath Group Title
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    Re-read the problem and tell me if we have answered the question yet.

    • 2 years ago
  35. erica123 Group Title
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    i did but i don't know won't that only find x and not y?

    • 2 years ago
  36. SmoothMath Group Title
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    Right. Well actually, it finds y. Right?

    • 2 years ago
  37. erica123 Group Title
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    i think so?

    • 2 years ago
  38. SmoothMath Group Title
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    We wrote our two equations. We substituted into one of them and got an equation with just one variable, y. We're now using the quadratic formula to solve for that variable. It's a little bit confusing because we're getting two possibilities for that variable, but we're still only solving for the one variable. We don't know the second variable yet.

    • 2 years ago
  39. erica123 Group Title
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    yes it seems so confusing i got fractions for both answers -1/12 and 1/20 is that correct?

    • 2 years ago
  40. SmoothMath Group Title
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    =/ I don't know what mistake you made.

    • 2 years ago
  41. erica123 Group Title
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    i dont know either :(

    • 2 years ago
  42. SmoothMath Group Title
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    \[\frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-(-8) \pm \sqrt{(-8)^2-4(4)(-60)}}{2(4)}\]

    • 2 years ago
  43. SmoothMath Group Title
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    You probably just messed up on a sign somewhere. Did you plug in like that?

    • 2 years ago
  44. erica123 Group Title
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    oh i see what i did im sorry i was doing 2ac instead of 2a

    • 2 years ago
  45. SmoothMath Group Title
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    Ah =)

    • 2 years ago
  46. erica123 Group Title
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    x= 5 and x= -3?

    • 2 years ago
  47. SmoothMath Group Title
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    Good. Except we were solving for y. It's important because of the next step.

    • 2 years ago
  48. SmoothMath Group Title
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    When I go back and plug into the original equation, I want to make sure I plug into the right variable.

    • 2 years ago
  49. erica123 Group Title
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    which variable do i plug into and do i use the 5 or -3?

    • 2 years ago
  50. SmoothMath Group Title
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    Okay, when you do this kind of problem, it's not important which variable you solve for first. You picked y. That's fine. What's not fine is that halfway through the problem, you started calling it x. Do you understand? You were solving for y, and then you randomly renamed it x. This will cause problems. You solved for y. Don't rename it and there won't be any confusion. So now you know y, so obviously that's what you can substitute in for.

    • 2 years ago
  51. slaaibak Group Title
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    lol

    • 2 years ago
  52. erica123 Group Title
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    sorry and yes we know 2 answer to y so then which one would you substitute for x?

    • 2 years ago
  53. SmoothMath Group Title
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    Now, I understand that it's a little confusing that you get two answers for y. Try not to be confused by it. It just means that there are two possible answers to the question. One is when y=5 and the other is when y = -3. Whichever one you pick, you'll get an x value that goes along with that y value.

    • 2 years ago
  54. erica123 Group Title
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    ok i chose 5 and plugged it into x=4y-8 and i got 12

    • 2 years ago
  55. SmoothMath Group Title
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    Good =) So one possible solution is: x=12 y =5 Understand? Find the other possible solution.

    • 2 years ago
  56. erica123 Group Title
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    the other possible solution is 55?

    • 2 years ago
  57. SmoothMath Group Title
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    Woah there. Where'd 55 come from? You makin' guesses or somethin'?

    • 2 years ago
  58. erica123 Group Title
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    whoops is it 63?

    • 2 years ago
  59. erica123 Group Title
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    wait ! lol sorry im using the wrong equation

    • 2 years ago
  60. SmoothMath Group Title
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    I have no idea what you're doing. Lol.

    • 2 years ago
  61. erica123 Group Title
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    x= -20 ?

    • 2 years ago
  62. SmoothMath Group Title
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    That's not wrong... but it's not a complete answer.

    • 2 years ago
  63. erica123 Group Title
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    but isnt it x= 12, -20

    • 2 years ago
  64. SmoothMath Group Title
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    The question asks you what the two variables are. The two variables are x and y. It turns out this problem has two possible answers, but a good answer should give me an x value and a y value.

    • 2 years ago
  65. erica123 Group Title
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    but theres 2 x and y values

    • 2 years ago
  66. SmoothMath Group Title
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    Ooooh, goodness. How to explain this...

    • 2 years ago
  67. erica123 Group Title
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    lol i dont know what should i do? should i just leave 2 values for both variables?

    • 2 years ago
  68. SmoothMath Group Title
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    Kind of.

    • 2 years ago
  69. SmoothMath Group Title
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    Alright, stop worrying so much about the correct answer and let's just consider the question, okay?

    • 2 years ago
  70. erica123 Group Title
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    ok

    • 2 years ago
  71. SmoothMath Group Title
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    The question is talking about a couple of numbers. We called them x and y. And it told us something about those numbers.

    • 2 years ago
  72. SmoothMath Group Title
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    It told us that that their product is 60. We wrote an equation about that. And it told us that one number was 8 less than 4 times the other. We wrote an equation about that.

    • 2 years ago
  73. slaaibak Group Title
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    Two solution sets. (5,12) and (-3, 20) That's all you need to know

    • 2 years ago
  74. SmoothMath Group Title
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    And we're just trying to figure out two numbers that those things are true for.

    • 2 years ago
  75. SmoothMath Group Title
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    Right?

    • 2 years ago
  76. erica123 Group Title
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    right

    • 2 years ago
  77. SmoothMath Group Title
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    So our answer should be two numbers. We happened to name them x and y, so our answer will look like x= y=

    • 2 years ago
  78. SmoothMath Group Title
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    Well, it turns out, there's more than one possible pair of numbers.

    • 2 years ago
  79. erica123 Group Title
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    yup so i just leave those 2 answers?

    • 2 years ago
  80. SmoothMath Group Title
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    Right. And what are those two answers?

    • 2 years ago
  81. erica123 Group Title
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    y= 5, -3 x= 12, -20

    • 2 years ago
  82. SmoothMath Group Title
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    mmmm, I don't like how you wrote that.

    • 2 years ago
  83. erica123 Group Title
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    why?

    • 2 years ago
  84. SmoothMath Group Title
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    Is x=5 y = -20 a solution?

    • 2 years ago
  85. SmoothMath Group Title
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    Try plugging it in if you need to check.

    • 2 years ago
  86. erica123 Group Title
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    no i put y=5

    • 2 years ago
  87. erica123 Group Title
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    and x= -20

    • 2 years ago
  88. SmoothMath Group Title
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    Sorry, my mistake. Is y = 5 x=-20 a solution?

    • 2 years ago
  89. SmoothMath Group Title
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    That's what I meant to ask.

    • 2 years ago
  90. erica123 Group Title
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    wait no it isnt i just tried it out

    • 2 years ago
  91. SmoothMath Group Title
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    Oh my. =(

    • 2 years ago
  92. SmoothMath Group Title
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    Okay so... is y=5 still good?

    • 2 years ago
  93. SmoothMath Group Title
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    It's not good when x=-20, we decided.

    • 2 years ago
  94. erica123 Group Title
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    yes

    • 2 years ago
  95. SmoothMath Group Title
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    Alright, why is it still good?

    • 2 years ago
  96. erica123 Group Title
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    because when we plug it in -20=4(5)-8 it gives us 12 which is not equal to -20

    • 2 years ago
  97. SmoothMath Group Title
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    Okay, that tells me why y=5 x=-20 is not a solution. Is y =5 bad in general then? Is x=-20 bad?

    • 2 years ago
  98. erica123 Group Title
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    yes its bad the -20

    • 2 years ago
  99. erica123 Group Title
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    wait no the 5 is bad

    • 2 years ago
  100. erica123 Group Title
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    if we plug in -3 it will work

    • 2 years ago
  101. SmoothMath Group Title
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    Ahhhhhh my point isn't that they are bad COMPLETELY. My point is just that they don't work TOGETHER.

    • 2 years ago
  102. erica123 Group Title
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    oh sorry lol so i can just leave both numbers?

    • 2 years ago
  103. SmoothMath Group Title
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    Your answer really needs to be two numbers that work together. What are two numbers that work together?

    • 2 years ago
  104. erica123 Group Title
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    -3 and -20

    • 2 years ago
  105. SmoothMath Group Title
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    Great. That's one answer.

    • 2 years ago
  106. SmoothMath Group Title
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    As a SECOND. SEPARATE answer

    • 2 years ago
  107. SmoothMath Group Title
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    you could do 5 and 12

    • 2 years ago
  108. SmoothMath Group Title
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    So, to clarify, you wrote y = 5, -3 x = 12, -20 Which doesn't make it obvious which number goes with which. If you write it this way, it's much more clear y=5 x=12, and y=-3 x=-20

    • 2 years ago
  109. SmoothMath Group Title
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    I know it probably seems unimportant, but writing it the first way really shows that you don't understand the question or your answer.

    • 2 years ago
  110. erica123 Group Title
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    no it does seem important, thanks so much once again for your help it really means alot =D but i must go because its getting pretty late here

    • 2 years ago
  111. SmoothMath Group Title
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    Well, if the problem was written as an actual real-life problem, it would be easier to explain why it was important. For example, maybe these numbers we're trying to solve for are x=pack of skittles purchased y = number of snickers bars purchased My answer would say something like "Oh, you EITHER bought 5 packs of skittles and 12 snickers bars OOOOR you bought -3 packs of skittles and -20 snickers bars" (shhh please ignore the fact that you can't buy a negative numer of snicker bars) Your answer would say something like, "You bought 5 packs of skittles and -3 packs of skittles. And the number of snickers bars you bought is 12. And also -20."

    • 2 years ago
  112. erica123 Group Title
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    oh yeahhh! i like how you related it to real life lol and yeah so it really is possible to have negatives in our answer as long as it works together

    • 2 years ago
  113. SmoothMath Group Title
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    Yeah, we can have negatives =) If we're solving real life problems, a lot of times we'll get negative answers. Those negative answers might make sense, or they might not and we might ignore them.

    • 2 years ago
  114. SmoothMath Group Title
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    For example, if our problem was about money, then the positive answer might mean we made money and the negative answer might mean we lost money. However, if the problem we're solving is about how many children someone has and we got one negative answer and one positive answer, well we'd take the positive one and ignore the negative one because there is no way to have negative children.

    • 2 years ago
  115. erica123 Group Title
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    yeah i see where you're going at and what you'tr trying to say. im sorry to end this convo but i have to leave to get some sleep because im up early in the morning tomorrow

    • 2 years ago
  116. SmoothMath Group Title
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    Goodnight. =)

    • 2 years ago
  117. erica123 Group Title
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    goodnight and thanks so much once again! you have been an amazing help!

    • 2 years ago
  118. SmoothMath Group Title
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    My pleasure =)

    • 2 years ago
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