Q: Find the positive number that satisfies the following conditions: (1) two-thirds of the number is equal to 16/216 of its reciprocal, and (2) the number is positive

A 4/12
B 5/21
C 14/12
D 9/25
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Answer: A

Letting the positive number be x and then expressing the first condition in terms of x, we get:

2/3 x = 16/216 * 1/x

We can then multiply both sides by 216 and simplify to get:

x^2 = 16/144

Taking the square root of both sides gives:

x = sqrt(16/144)

Simplifying this expression gives:

x = sqrt(1/9)

Finally, since the number must be positive, we take the positive square root, which gives us:

x = 1/3 or 4/12

Therefore, the positive number that satisfies the given conditions is 1/3.

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