29.3k views
5 votes
If y varies inversely as x and y=2 when x=8, find x when y =14

User Cherif
by
7.9k points

1 Answer

4 votes

When we have the statement " y varies inversely as x ". We have the next equation:


y=(k)/(x)

Where k represents the constant between them.

Replace using the given values:

y=2

x=8


2=(k)/(8)

Now, solve for k:

Multiply both sides by 8


\begin{gathered} 8\cdot2=8\cdot(k)/(8) \\ 16=k \end{gathered}

Hence, the constant value k is equal to 16.

Let's find x where y=14 and k =16.

Use the same equation to find x and replace it with the given values:


\begin{gathered} 14=(16)/(x) \\ \text{Multiply both sides by x} \\ x\cdot14=x\cdot(16)/(x) \\ \text{Simplify} \\ 14x=16 \\ \text{Now, divide both sides by 14} \end{gathered}
\begin{gathered} (14)/(14)x=(16)/(14) \\ x=(8)/(7) \end{gathered}

Hence, when y=14, the x value will be 8/7

User Ryan Buening
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories