Question

Suppose c and d vary inversely, and d=2 when c = 17.1. Write an equation that models the variation.2. Find d when c = 68

Answer 1

1. Given that "c" and "d" vary inversely, you need to remember that the form of an equation of an Inverse Variation is:

`y=(k)/(x)`

Or, in this case:

`d=(k)/(c)`

Where "k" is the Constant of variation.

Knowing that:

`d=2`

When:

`c=17`

You can substitute values into the equation and solve for "k":

`\begin{gathered} 2=(k)/(17) \\ \\ 2\cdot17=k \\ \\ k=34 \end{gathered}`

Now you know that the equation that models the variation is:

`d=(34)/(c)`

2. In order to find the value of "d" when:

`c=68`

You need to substitute that value into the equation and then evaluate:

`\begin{gathered} d=(34)/(68) \\ \\ d=(1)/(2) \end{gathered}`

Hence, the answers are:

1.

`d=(34)/(c)`

2.

`d=(1)/(2)`