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Math Expert V
Joined: 02 Sep 2009
Posts: 59124
A candle company determines that, for a certain specialty candle, the  [#permalink]

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5
23 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:52) correct 29% (01:55) wrong based on 834 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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3
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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Senior Manager  Joined: 02 Mar 2012
Posts: 269
Schools: Schulich '16
Re: A candle company determines that, for a certain specialty candle, the  [#permalink]

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2
C for me .

equation you get is:

x(m1-m2)=b2-b1

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

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1
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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Re: A candle company determines that, for a certain specialty candle, the  [#permalink]

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(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

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

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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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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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@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.
Manager  S
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A candle company determines that, for a certain specialty candle, the  [#permalink]

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@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.

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

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