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If the price of a commodity is directly proportional to m^3 [#permalink]

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07 Apr 2013, 04:45

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If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity?

A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity? A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

Let the price is P & constant is K So P = \(\frac{K m^3}{q^2}\)

Now Just use the values in the options and put in the before mentioned equation. A) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 3^3}{2^2}\) = \(\frac{K 27}{4}\) = 6.75 K B) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 12^3}{12^2}\) = 12 K C) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 20^3}{20^2}\) = 20 K D) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 30^3}{36^2}\) = 125/6 = >20K E) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 36^3}{72^2}\) = 9 K

So the answer is D. This is probably 600-700 level question.

Hope the explanation helps.
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Last edited by emmak on 07 Apr 2013, 05:00, edited 1 time in total.

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity? A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

Function = \(\frac{m^3}{q^2}\)

A=\(\frac{3*3*3}{2*2}=\frac{27}{4}=7\) almost B=\(\frac{12*12*12}{12*12}=12\) C=\(\frac{20*20*20}{20*20}=20\) D=\(\frac{30*30*30}{36*36}=125/6\) E=\(\frac{36*36*36}{72*72}=9\)

It's down to C or D, because \(\frac{120}{6}=20\), \(\frac{125}{6}>20\) D _________________

It is beyond a doubt that all our knowledge that begins with experience.

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity?

A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

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09 Apr 2013, 03:56

Let price of the commodity be P = \(k *\)\(m^3\) /\(Q^2\)

A. P = \(k * 27/4\) = 6.75K B. P = \(K * 12^3/12^2\) = 12k C. P = \(K * 20^3/20^2\) = 20k D. P = \(K * 30^3/36^2\)= \(k*5*5*30/6*6\) = \(k * (125/6)\) = 21K (approx) E. P = \(k * 36^3/72^2\) = \(K*(36/2*2)\) = 9k

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

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10 Apr 2013, 17:09

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Could you please explain how you get \(\frac{m^3}{q^2}\) or \(\frac{Km^3}{q^2}\)? Where am I wrong expressing this thing firstly as \(p=m^3k\) and \(p=\frac{k}{q^2}\)?
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Re: If the price of a commodity is directly proportional to m^3 [#permalink]

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10 Apr 2013, 22:19

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obs23 wrote:

Could you please explain how you get \(\frac{m^3}{q^2}\) or \(\frac{Km^3}{q^2}\)? Where am I wrong expressing this thing firstly as \(p=m^3k\) and \(p=\frac{k}{q^2}\)?

"directly proportional to m^3 and inversely proportional to q^2" is what the text says. So if m increases the price increases, if q increases the price decreases. The right formula here is \(\frac{m^3}{q^2}\) ( or with k, it doesn`t change anything), if the numerator grows, the price does the same; and as in every fraction, if the denominator grows, the price drops. Your formulas are right but the price depends on both m and q, you have to include them in one equation.

Let me know if it is clear
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Re: If the price of a commodity is directly proportional to m^3 [#permalink]

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11 Apr 2013, 02:51

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Zarrolou wrote:

obs23 wrote:

Could you please explain how you get \(\frac{m^3}{q^2}\) or \(\frac{Km^3}{q^2}\)? Where am I wrong expressing this thing firstly as \(p=m^3k\) and \(p=\frac{k}{q^2}\)?

"directly proportional to m^3 and inversely proportional to q^2" is what the text says. So if m increases the price increases, if q increases the price decreases. The right formula here is \(\frac{m^3}{q^2}\) ( or with k, it doesn`t change anything), if the numerator grows, the price does the same; and as in every fraction, if the denominator grows, the price drops. Your formulas are right but the price depends on both m and q, you have to include them in one equation.

Let me know if it is clear

I see that makes sense. I guess I am making it more complicated than it really is. If you say that my formulas are correct, then \(\frac{m^3}{q^2}\) should somehow be extracted from \(p=m^3k\) and \(p=\frac{k}{q^2}\), no? Technically speaking, I thought there was a way to combine them into \(\frac{m^3}{q^2}\), just from pure algebraic manipulation (which I am very interested in here)... Or is it simply about common sense or the way you explained it?

P.S. Like your "kudos" tagline man!
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Re: If the price of a commodity is directly proportional to m^3 [#permalink]

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11 Apr 2013, 03:05

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obs23 wrote:

I see that makes sense. I guess I am making it more complicated than it really is. If you say that my formulas are correct, then \(\frac{m^3}{q^2}\) should somehow be extracted from \(p=m^3k\) and \(p=\frac{k}{q^2}\), no? I thought there was a way to combine them into \(\frac{m^3}{q^2}\), just from pure algebraic manipulation (which I am very interested in here)... Or is it simply about common sense or the way you explained it?

P.S. Like your tagline man!

To create the formula we should refer to the text: "If the price of a commodity is directly proportional to m^3 [and at this point we write down Price= \(m^3\)] andinversely proportional to q^2 [and at this point we complete the foumula adding the Denominator so Price=\(\frac{m^3}{q^2}\)], which of the following values of m and q will result in the highest price for the commodity?" \(\frac{m^3}{q^2}\) is not extracted from \(p=m^3k\) and \(p=\frac{k}{q^2}\), and you cannot obtain it from pure algebraic manipulation. The idea behind your formulas is correct p=m^3 expresses the direct correlation between p and m; and also p=1/q^2 expresses the inverse correlation between p and q. But the text uses "and" so those ideas must be expressed in one formula, so to obtain this final formula you "complete" one with the other =>m^3/p^2
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It is beyond a doubt that all our knowledge that begins with experience.

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity?

A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

For more on direct, inverse and joint variation, check out these posts:

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

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