swerve wrote: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 x is directly proportional to y and inversely proportional to z. the following equation is implied:
x = k(y/z), where k is a constant.
The price of a commodity is directly proportional to \(m^3\) and inversely proportional to \(q^2\).
Thus:
p = k(m³/q²), where k is a constant.
Let k = 1, implying that p = m³/q².
When the question stem includes the phrase
which of the following, the correct answer is likely D or E.
E: p = 36³/72² = (36/72)² * 36 = 1/4 * 36 = 9
D: p = 30³/36² = (30/36)² * 30 = (5/6)² * 30 = (5²/6)(5) = 125/6 = more than 20
Eliminate E, since D is greater.
C: p = 20³/20² = (20/20)² * 20 = 20
Eliminate C, since D is greater.
B: p = 12³/12² = (12/12)² * 12 = 12
Eliminate B, since D is greater.
A: p = 3³/2² = 27/4
Eliminate A, since D is greater.
The correct answer is
D.
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