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# A candle company determines that, for a certain specialty candle, the

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Math Expert
Joined: 02 Sep 2009
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A candle company determines that, for a certain specialty candle, the  [#permalink]

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03 Jul 2016, 10:47
4
12
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:34) correct 28% (01:34) wrong based on 447 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  [#permalink]

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03 Jul 2016, 20:45
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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
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##### General Discussion
Senior Manager
Joined: 02 Mar 2012
Posts: 326
Schools: Schulich '16
Re: A candle company determines that, for a certain specialty candle, the  [#permalink]

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03 Jul 2016, 23:16
C for me .

equation you get is:

x(m1-m2)=b2-b1

1+2 is needed for value of x
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Re: A candle company determines that, for a certain specialty candle, the  [#permalink]

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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

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Joined: 17 Nov 2014
Posts: 51
Location: India
Re: A candle company determines that, for a certain specialty candle, the  [#permalink]

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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
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Re: A candle company determines that, for a certain specialty candle, the  [#permalink]

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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 (m1-m2)x=b2-b1, 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  [#permalink]

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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.
A candle company determines that, for a certain specialty candle, the &nbs [#permalink] 14 Apr 2018, 06:21
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