Solution:

Identify the given values and the required value:

Given: p::9:4
Required: p/s

Understand the concept of continued proportion:

In a continued proportion, the product of the extremes is equal to the product of the means. That is, if a:b::c:d, then a*d = b*c.

Apply the concept to the given values:

We have p::9:4, which means p/9 = 9/4, because the first and second terms are in the same ratio as the second and third terms. Solving for p, we get p = 81/4.

Now, we need to find p/s. We know that p*s = 81/4 * s, but we don't know the value of s. However, we can use the fact that p::9:4 to find s.

Using the concept of continued proportion, we have p/9 = 9/4, which means p = 81/4 and 9/4 = s/p. Solving for s, we get s = 81/4 * 9/4 = 81/16.

Finally, we can find p/s by dividing p by s:

p/s = (81/4)/(81/16) = 16/4 = 4.

Therefore, p/s = 4.

Conclusion:

To find p/s when p::9:4, we need to use the concept of continued proportion and the fact that the product of the extremes is equal to the product of the means. We can then solve for the missing values and use them to find p/s.

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