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# The cost per kg of rice varies inversely with the square of the quanti

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Math Expert
Joined: 02 Sep 2009
Posts: 61396
The cost per kg of rice varies inversely with the square of the quanti  [#permalink]

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16 Jan 2020, 03:19
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Difficulty:

35% (medium)

Question Stats:

79% (01:38) correct 21% (01:54) wrong based on 33 sessions

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The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?

A. 5 million tons
B. 5.25 million tons
C. 5.5 million tons
D. 5.75 million tons
E. 6 million tons

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Re: The cost per kg of rice varies inversely with the square of the quanti  [#permalink]

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16 Jan 2020, 07:37
given
x = 36* 49
x= 1764
now
1764/49 = x^2
x= 6
IMO E

Bunuel wrote:
The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?

A. 5 million tons
B. 5.25 million tons
C. 5.5 million tons
D. 5.75 million tons
E. 6 million tons
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Posts: 9443
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Re: The cost per kg of rice varies inversely with the square of the quanti  [#permalink]

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18 Jan 2020, 12:49
1
Bunuel wrote:
The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?

A. 5 million tons
B. 5.25 million tons
C. 5.5 million tons
D. 5.75 million tons
E. 6 million tons

Recall that if y varies inversely with x, we let k = the constant of proportionality and we set up the following equation:

y = k * (1/x)

If y varies inversely with the square of x, then the equation is modified to:

y = k * (1/(x^2))

For this question, let’s let c = the cost per kg of rice and q = the quantity produced. Thus, we have:

c = k * (1/(q^2))

36 = k * (1/(7^2))

36 = k * (1/49)

36 * 49 = k

k = 36 * 49 (Note that we do not perform the final multiplication here.)

Now we can let x = the number of millions of tons of rice produced such that the cost was \$49/kg and create the equation:

49 = k * (1/(x^2))

49 = 36 * 49 * (1/(x^2))

1/36 = (1/(x^2))

x^2 = 36

x = 6 million tons

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Re: The cost per kg of rice varies inversely with the square of the quanti   [#permalink] 18 Jan 2020, 12:49
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