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

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

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New post 03 Jul 2016, 10:47
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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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New post 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
Answer C
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Re: A candle company determines that, for a certain specialty candle, the  [#permalink]

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New post 03 Jul 2016, 23:16
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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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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 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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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 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.

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

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New post 21 May 2019, 12:09
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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 y-intercepts. Insufficient.

(2) \(b_2 – b_1 = 6\)
We have the y-intercepts 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  [#permalink]

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New post 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
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A candle company determines that, for a certain specialty candle, the   [#permalink] 23 Jun 2019, 06:13
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