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If pp and qq vary inversely and pp is 30 when qq is 25, determine qq when pp is equal to 50.

If pp and qq vary inversely and pp is 30 when qq is 25, determine qq when pp is equal-example-1
User Frankodwyer
by
2.2k points

1 Answer

21 votes
21 votes

The Solution:

Given that p and q are inversely related, we have that:


p\propto(1)/(q)

This means that:


\begin{gathered} p=(1)/(q)* k \\ \\ p=(k)/(q) \\ \\ \text{ Where k=constant of variation.} \end{gathered}

Given the initial condition (or values) that p =30 when q = 25.

Substituting these values in the relation above, we get


30=(k)/(25)

Cross multiplying, we get


k=30*25=750

So, the formula connecting p and q is obtained as


p=(750)/(q)

We are asked to find the value of q when p = 50.

Substitute 50 for p in the formula connecting p and q.


50=(750)/(q)

Cross multiplying, we get


50q=750

Dividing both sides by 50, we get


\begin{gathered} (50q)/(50)=(750)/(50) \\ \\ q=15 \end{gathered}

Therefore,

User Nagaraju Badaeni
by
2.9k points