Discussion
If \(\frac{3}{2} : \frac{1}{p} = \frac{1}{p} : \frac{1}{6}\), then the value of p (p \gt 0) is:
Answer: A
The value of p is 2. In a proportion the product of the means equals the product of the extremes. \[\frac{3}{2} \times \frac{1}{6} = \frac{1}{p} \times \frac{1}{p}\\\] \[\frac{1}{4} = \frac{1}{p^2}\] so \(p^2 = 4\), and since p is positive, p = 2. Check: 3/2 : 1/2 = 3 : 1 and 1/2 : 1/6 = 3 : 1, so the two ratios are equal. The other options 3, 3.5 and 4 give squares of 9, 12.25 and 16 instead of 4.
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