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Math Expert
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A candle company determines that, for a certain specialty candle, the
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03 Jul 2016, 10:47
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71% (01:52) correct 29% (01:55) wrong based on 816 sessions
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A candle company determines that, for a certain specialty candle, the supply function is \(p = m_1*x + b_1\) and the demand function is \(p = m_2*x + b_2\), where p is the price of each candle, x is the number of candles supplied or demanded, and \(m_1\), \(m_2\), \(b_1\), and \(b_2\) are constants. At what value of x do the graphs of the supply function and demand function intersect? (1) \(m_1 = m_2 = 0.005\) (2) \(b_2 – b_1 = 6\)
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Re: A candle company determines that, for a certain specialty candle, the
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03 Jul 2016, 20:45
Bunuel wrote: A candle company determines that, for a certain specialty candle, the supply function is \(p = m_1*x + b_1\) and the demand function is \(p = m_2*x + b_2\), where p is the price of each candle, x is the number of candles supplied or demanded, and \(m_1\), \(m_2\), \(b_1\), and \(b_2\) are constants. At what value of x do the graphs of the supply function and demand function intersect?
(1) \(m_1 = m_2 = 0.005\) (2) \(b_2 – b_1 = 6\) supply function is \(p = m_1*x + b_1\) demand function is \(p = m_2*x + b_2\) At the point of intersection , the lines will have same value of p . Therefore , we can set the equations equal to each other . \(m_1*x + b_1 = m_2*x + b_2\) (1) \(m_1 = m_2 = 0.005\) Not sufficient as we have no information about \(b_1\) and \(b_2\) (2) \(b_2 – b_1 = 6\) Not sufficient as we have no information about \(m_1\) and \(m_2\) Combining 1 and 2 ,we get Sufficient Answer C
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Re: A candle company determines that, for a certain specialty candle, the
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03 Jul 2016, 23:16
C for me .
equation you get is:
x(m1m2)=b2b1
1+2 is needed for value of x



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Re: A candle company determines that, for a certain specialty candle, the
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06 Jul 2016, 11:41
(1) \(m_1 = m_2 = 0.005\) Not sufficient as we have no information about \(b_1\) and \(b_2\)
(2) \(b_2 – b_1 = 6\) Not sufficient as we have no information about \(m_1\) and \(m_2\) Combining , Sufficient
Answer C



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Re: A candle company determines that, for a certain specialty candle, the
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10 Jul 2016, 16:41
supply function p=m1∗x+b1p=m1∗x+b1 demand function p=m2∗x+b2p=m2∗x+b2
At the point of intersection , the lines will have same value of p . Therefore , we can set the equations equal to each other . m1∗x+b1=m2∗x+b2m1∗x+b1=m2∗x+b2 ( 4 varaibles i.e \(m1, m2, b1,b2)\)
Statement 1 : m1=−m2=0.005m1=−m2=0.005 Not sufficient as we have no information about b1 and b2
Statement 2: \(b2–b1\)=6b2–b1=6 Not sufficient as we have no information about m1 and m2
Combining 1 and 2 ,we get the value of \(X\) Sufficient Answer C



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Re: A candle company determines that, for a certain specialty candle, the
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02 Nov 2016, 07:25
My approach: at the pt. of intersection we will have values of p & x equal, further solving m1x+ b1=m2x+ b2, which implies (m1m2)x=b2b1, to get value of x we need both a & b and subsequently value of y through reverse substitutions. Can there be a conceptual / qualitative approach as well...or i am right in this approach?



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A candle company determines that, for a certain specialty candle, the
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14 Apr 2018, 06:21
@Bunuel,@Veritasprepkarishma, I know where 2 lines intersect, the value of P should be same but could you please how value of P could be same or not for this problem? Thanks.



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A candle company determines that, for a certain specialty candle, the
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03 Oct 2018, 12:02
sadikabid27 wrote: @Bunuel,@Veritasprepkarishma, I know where 2 lines intersect, the value of P should be same but could you please how value of P could be same or not for this problem? Thanks. Dear sadikabid27, The equation given here is the equation of a line \(y = mx+c\) For any 2 lines to intersect the x and y coordinates need to be the same, otherwise they would not interest. So as the statement mentions : Quote: At what value of x do the graphs of the supply function and demand function intersect? Which means value of x is same for both the equations, all we need to do is put the value of y as same, P in this case. I hope this helps.
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Re: A candle company determines that, for a certain specialty candle, the
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18 Oct 2018, 08:58
Bunuel wrote: A candle company determines that, for a certain specialty candle, the supply function is \(p = m_1*x + b_1\) and the demand function is \(p = m_2*x + b_2\), where p is the price of each candle, x is the number of candles supplied or demanded, and \(m_1\), \(m_2\), \(b_1\), and \(b_2\) are constants. At what value of x do the graphs of the supply function and demand function intersect?
(1) \(m_1 = m_2 = 0.005\) (2) \(b_2 – b_1 = 6\) They will intersect when they are equal. \(m_1*x + b_1 = m_2*x + b_2\) this can be rewritten as \(m_1*x  m_2 *x = b_2  b_1\) From statement 1) we have only one side of the equation the \(m_1 and the m_2\) value. Insufficient From statement 2) we have only one side of the equation the \(b_2  b_1\). Insufficient. Combined we know both sides and as a result can find x. Sufficient. C



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Re: A candle company determines that, for a certain specialty candle, the
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21 May 2019, 12:09
Value Question: What is x when the two equations (lines) are set to be equal (intersect)?
(1) \(m_1 = m_2 = 0.005\) We have the slopes of the two lines, but no information about the yintercepts. Insufficient.
(2) \(b_2 – b_1 = 6\) We have the yintercepts of the two lines, but no information about the slopes. Insufficient.
(3) We have 1 variable and 1 equation, we can find x. Sufficient. line 1 = 0.005x + b1 line 2 = 0.005x + b1 + 6  set equal and remove b1 constant 0.005x = 0.005x + 6 0.01x = 6 x = 600



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A candle company determines that, for a certain specialty candle, the
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23 Jun 2019, 06:13
At the point of intersection , the lines will have same value of p . m1∗x+b1=m2∗x+b2
(1) m1=−m2=0.005 Not sufficient as we have no information about b1b1 and b2b2 (2) b2–b1=6b2–b1=6 Not sufficient as we have no information about m1m1 and m2m2 Answer C




A candle company determines that, for a certain specialty candle, the
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23 Jun 2019, 06:13






