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erica123

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

  • one year ago
  • one year ago

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

    • one year ago
  2. erica123
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    can you help solve it?

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

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

    • one year ago
  5. SmoothMath
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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.

    • one year ago
  6. erica123
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    i got y=-15 and x=-68?

    • one year ago
  7. erica123
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    im not positive that thats correct

    • one year ago
  8. SmoothMath
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    no =( I don't think so.

    • one year ago
  9. slaaibak
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    Try again.

    • one year ago
  10. erica123
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    i dont know what i did wrong :/

    • one year ago
  11. SmoothMath
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    Show me your work, okay?

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

    • one year ago
  13. slaaibak
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    The problem lies in line 2

    • one year ago
  14. erica123
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    x= 4(-15)-8 x= -60-8 x=-68

    • one year ago
  15. erica123
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    what the problem? :o

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

    • one year ago
  17. SmoothMath
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    distribute, sweet thang.

    • one year ago
  18. erica123
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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

    • one year ago
  19. SmoothMath
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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?

    • one year ago
  20. erica123
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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

    • one year ago
  21. SmoothMath
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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.

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

    • one year ago
  23. erica123
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    2 and 2

    • one year ago
  24. SmoothMath
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    It makes it a lot easier.

    • one year ago
  25. SmoothMath
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    Nooo show me your factoring, please.

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

    • one year ago
  27. SmoothMath
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    noope. show me your factoring.

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

    • one year ago
  29. erica123
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    4y*y ?

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

    • one year ago
  31. erica123
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    ok

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

    • one year ago
  33. erica123
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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?

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

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

    • one year ago
  36. SmoothMath
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    Right. Well actually, it finds y. Right?

    • one year ago
  37. erica123
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    i think so?

    • one year ago
  38. SmoothMath
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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.

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

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

    • one year ago
  41. erica123
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    i dont know either :(

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

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

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

    • one year ago
  45. SmoothMath
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    Ah =)

    • one year ago
  46. erica123
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    x= 5 and x= -3?

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

    • one year ago
  48. SmoothMath
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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.

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

    • one year ago
  50. SmoothMath
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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.

    • one year ago
  51. slaaibak
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    lol

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

    • one year ago
  53. SmoothMath
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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.

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

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

    • one year ago
  56. erica123
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    the other possible solution is 55?

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

    • one year ago
  58. erica123
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    whoops is it 63?

    • one year ago
  59. erica123
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    wait ! lol sorry im using the wrong equation

    • one year ago
  60. SmoothMath
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    I have no idea what you're doing. Lol.

    • one year ago
  61. erica123
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    x= -20 ?

    • one year ago
  62. SmoothMath
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    That's not wrong... but it's not a complete answer.

    • one year ago
  63. erica123
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    but isnt it x= 12, -20

    • one year ago
  64. SmoothMath
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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.

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

    • one year ago
  66. SmoothMath
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    Ooooh, goodness. How to explain this...

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

    • one year ago
  68. SmoothMath
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    Kind of.

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

    • one year ago
  70. erica123
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    ok

    • one year ago
  71. SmoothMath
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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.

    • one year ago
  72. SmoothMath
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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.

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

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

    • one year ago
  75. SmoothMath
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    Right?

    • one year ago
  76. erica123
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    right

    • one year ago
  77. SmoothMath
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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=

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

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

    • one year ago
  80. SmoothMath
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    Right. And what are those two answers?

    • one year ago
  81. erica123
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    y= 5, -3 x= 12, -20

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

    • one year ago
  83. erica123
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    why?

    • one year ago
  84. SmoothMath
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    Is x=5 y = -20 a solution?

    • one year ago
  85. SmoothMath
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    Try plugging it in if you need to check.

    • one year ago
  86. erica123
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    no i put y=5

    • one year ago
  87. erica123
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    and x= -20

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

    • one year ago
  89. SmoothMath
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    That's what I meant to ask.

    • one year ago
  90. erica123
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    wait no it isnt i just tried it out

    • one year ago
  91. SmoothMath
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    Oh my. =(

    • one year ago
  92. SmoothMath
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    Okay so... is y=5 still good?

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

    • one year ago
  94. erica123
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    yes

    • one year ago
  95. SmoothMath
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    Alright, why is it still good?

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

    • one year ago
  97. SmoothMath
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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?

    • one year ago
  98. erica123
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    yes its bad the -20

    • one year ago
  99. erica123
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    wait no the 5 is bad

    • one year ago
  100. erica123
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    if we plug in -3 it will work

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

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

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

    • one year ago
  104. erica123
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    -3 and -20

    • one year ago
  105. SmoothMath
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    Great. That's one answer.

    • one year ago
  106. SmoothMath
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    As a SECOND. SEPARATE answer

    • one year ago
  107. SmoothMath
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    you could do 5 and 12

    • one year ago
  108. SmoothMath
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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

    • one year ago
  109. SmoothMath
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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.

    • one year ago
  110. erica123
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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

    • one year ago
  111. SmoothMath
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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."

    • one year ago
  112. erica123
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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

    • one year ago
  113. SmoothMath
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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.

    • one year ago
  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.

    • one year ago
  115. erica123
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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

    • one year ago
  116. SmoothMath
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    Goodnight. =)

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

    • one year ago
  118. SmoothMath
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    My pleasure =)

    • one year ago
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