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erica123

  • 2 years ago

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

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  1. slaaibak
    • 2 years ago
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    Call the one integer x. call the other one y x = 4y - 8 xy = 60 Solve this.

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

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

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

  5. SmoothMath
    • 2 years ago
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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.

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

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

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

  9. slaaibak
    • 2 years ago
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    Try again.

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

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

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

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

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

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

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

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

  18. erica123
    • 2 years ago
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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

  19. SmoothMath
    • 2 years ago
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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?

  20. erica123
    • 2 years ago
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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

  21. SmoothMath
    • 2 years ago
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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.

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

  23. erica123
    • 2 years ago
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    2 and 2

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

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

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

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

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

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

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

  31. erica123
    • 2 years ago
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    ok

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

  33. erica123
    • 2 years ago
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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?

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

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

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

  37. erica123
    • 2 years ago
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    i think so?

  38. SmoothMath
    • 2 years ago
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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.

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

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

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

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

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

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

  45. SmoothMath
    • 2 years ago
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    Ah =)

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

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

  48. SmoothMath
    • 2 years ago
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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.

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

  50. SmoothMath
    • 2 years ago
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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.

  51. slaaibak
    • 2 years ago
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    lol

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

  53. SmoothMath
    • 2 years ago
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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.

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

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

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

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

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

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

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

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

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

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

  64. SmoothMath
    • 2 years ago
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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.

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

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

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

  68. SmoothMath
    • 2 years ago
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    Kind of.

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

  70. erica123
    • 2 years ago
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    ok

  71. SmoothMath
    • 2 years ago
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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.

  72. SmoothMath
    • 2 years ago
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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.

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

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

  75. SmoothMath
    • 2 years ago
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    Right?

  76. erica123
    • 2 years ago
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    right

  77. SmoothMath
    • 2 years ago
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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=

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

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

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

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

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

  83. erica123
    • 2 years ago
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    why?

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

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

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

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

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

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

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

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

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

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

  94. erica123
    • 2 years ago
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    yes

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

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

  97. SmoothMath
    • 2 years ago
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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?

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

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

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

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

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

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

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

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

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

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

  108. SmoothMath
    • 2 years ago
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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

  109. SmoothMath
    • 2 years ago
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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.

  110. erica123
    • 2 years ago
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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

  111. SmoothMath
    • 2 years ago
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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."

  112. erica123
    • 2 years ago
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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

  113. SmoothMath
    • 2 years ago
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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.

  114. SmoothMath
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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.

  115. erica123
    • 2 years ago
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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

  116. SmoothMath
    • 2 years ago
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    Goodnight. =)

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

  118. SmoothMath
    • 2 years ago
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    My pleasure =)

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