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## adl_thoo 2 years ago Since opening night, attendance at Play A has increased steadily, while attendance at Play B first rose and then fell. Equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. On what day(s) was the attendance the same at both plays? What was the attendance? Play A: y = 15x + 76 Play B: y = –x^2 + 36x – 4

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1. Luigi0210

You could set both equations equal to each other or graph and see where they intersect.

2. smokeydabear

Yes, all you are trying to do is find where the two graphs intersect, so setting the two equal to each other will give you the answer.

3. adl_thoo

is that my quickest way? i have 40 questions. and im only on 13.

4. Luigi0210

Yes, listen to Miss Bear :P

5. smokeydabear

Judging from your previous problems, I think your teacher is emphasizing the quadratic formula, so yes you will have to go through it once again =P

6. adl_thoo

UGH , it confuses me badly.

7. Luigi0210

I could give the solution if that'll help speed things along for you?

8. smokeydabear

It confuses you? What part of it confuses you?

9. adl_thoo

everything.

10. adl_thoo

The attendance was the same on day 5. The attendance was 151 at both plays on that day. The attendance was the same on day 16. The attendance was 316 at both plays on that day. The attendance was the same on days 5 and 16. The attendance at both plays on those days was 151 and 316 respectively. The attendance was never the same at both plays. these are my answer choices.

11. smokeydabear

It is a strategy used to figure out what value x has to be to make the quadratic equation equal to 0. Does that help?

12. smokeydabear

Honestly I am trying my hardest not to solve the problem, both for your practice and to fuel my laziness xD Luigi, would you like to solve it?

13. Luigi0210

Do you want a graph to help visual the equations?

14. adl_thoo

it doesnt matter. thats fine.

15. Luigi0210

It's kinda big sorry about the size

16. smokeydabear

Now that you see the intersecting points, you have to realize something about this problem. This is a problem that is using months for the x axis. Tell me why there is in reality only one solution to this problem?

17. adl_thoo

okat, hmmm...

18. smokeydabear

Don't overthink it, this is more of a common sense thing. Also, you could see the reason using the attendance number as well (y axis).

19. Luigi0210

If I solved it right, and I probably didn't but the exact answer would be $\frac{ -21+/-\sqrt{761} }{ 2}$

20. Luigi0210

But it would be the positive answer because you can't have negative units

21. adl_thoo

would it be C? The attendance was the same on days 5 and 16. The attendance at both plays on those days was 151 and 316 respectively.

22. smokeydabear

Look at what Luigi wrote. You can't have a negative number of people, or negative number of months for that matter.

23. Luigi0210

The points of intersection is (3.2931, 125.397)

24. adl_thoo

exactly. so answer C would be correct, right?

25. smokeydabear

I may just be looking at the graph wrong, but that shouldn't be it. C is telling you that there are two solutions to this problem. What Luigi and I were trying to tell you is that there is only one valid answer here.

26. smokeydabear

Are you understanding what I'm saying?

27. Luigi0210

So what the intersection points are say is that there are 125 people on day 3

28. Luigi0210

Are you understanding this or are getting more confused? :l

29. adl_thoo

more confused.

30. Luigi0210

I'm sorry ^_^' what specifically is confusing you?

31. smokeydabear

Okay think about it like this. If you were to take exactly what the graph told you as the solutions of the problem, you would have a negative number for something that can't be negative.

32. adl_thoo

a lot. idk why i think it is C .. idk ): is it B ?

33. smokeydabear

C would make sense if you were just trying to find solutions to the raw graphs, but we are looking at a real life scenario.

34. adl_thoo

exactly... so, would it change my answer to B ?

35. smokeydabear

I feel like it's A, because the point on the graph looks more like (5, 151) than (16, 316)

36. Luigi0210

You're probably thinking of it as a general graph like bear is saying. But think of it this way. When dealing with real life, is it possible to have negative audience and/or negative days?

37. adl_thoo

no.. so, a ,, is correct?

38. Luigi0210

And what are the solution choices? I must of missed them ._.

39. smokeydabear

It was (5, 151) for A, and (16, 316) for B. C said that both are true, and D said neither are true.

40. adl_thoo

yeah, what she said . ^_*

41. Luigi0210

I'd say D.

42. Luigi0210

But yet again she is the smart one here so..

43. smokeydabear

But what is bothering me is why they would consider (16, 316) as a possible solution. It's not even the negative solution... it's not anywhere on the graph xD

44. smokeydabear

Maybe the graph is wrong...

45. adl_thoo

ahhh , im confused. @primeralph , what would your input be on this question ?

46. Luigi0210

Oops, bear is right I used the wrong equation

47. Luigi0210

it is (5, 151)

48. adl_thoo

ohh goodness. so my answer is A ?

49. Luigi0210

I'm so sorry for messing this up D:

50. smokeydabear

Oh okay, but I just plugged the B coordinates into the original equations, and it worked.

51. smokeydabear

Let me try for A next.

52. Luigi0210

I'm so sorry for messing this up D:

53. primeralph

Imma just say, equate the two y's. Find an x. Then plug into any one of the equations.

54. adl_thoo

its fine.. & okay, ive gotten so confused. idk what to do :(

55. primeralph

@adl_thoo cheeel

56. smokeydabear

Okay I just confirmed that it is B

57. Luigi0210

And no you were right the answer is A or whatever the points are

58. smokeydabear

The graph threw me off, I just went brute force and plugged everything in, and only (16, 316) worked.

59. adl_thoo

so its B ?

60. smokeydabear

But aren't they equal at (16, 316)? Luigi, can you plug in the points into the equations to check?

61. Luigi0210

As it turns out both work :/

62. Luigi0210

So adl was right after all

63. smokeydabear

Oh look, my calculator was messing with me. Yes both work.

64. smokeydabear

My calculator never did like order of operations -.-

65. primeralph

|dw:1368580026141:dw|

66. primeralph

yo, was I too late?

67. Luigi0210

Naw :P

68. adl_thoo

noo . im still figuring this out.

69. smokeydabear

We were struggling for a long time and eventually got it, but your input helps reassure us, or me at least ^^

70. primeralph

plug in both 5 and 16 separately into eq A. That gives the number of people

71. adl_thoo

Sooo , wasit A B or C ?

72. Luigi0210

My stupidity has made this a bit harder than it needed to be

73. Luigi0210

and C

74. smokeydabear

It is C, because both work.

75. smokeydabear

That was extremely stressful...

76. adl_thoo

lol, itss, yay !! :D thanks guys.

77. primeralph

I don't know what the options are. It's really not stressful at all

78. adl_thoo

veryyyy !

79. primeralph

errr.............I knew what to do.............

80. adl_thoo

shoot, i didnt.

81. Luigi0210

It was just because I graphed the wrong equations :l

82. smokeydabear

It was only confusing because of Luigi's graph! >:0 But it's okay Luigi, I still wuv you <3

83. primeralph

so what did you get?

84. Luigi0210

Next time don't listen to me :P

85. adl_thoo

its okay guys :) we got it as The attendance was the same on days 5 and 16. The attendance at both plays on those days was 151 and 316 respectively.

86. primeralph

yeah

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