Question

An alligator's tail length, T, varies directly as its body length, B. An alligator with a bodylength of 2 feet has a tail length of 1.4 feet. What is the tail length of an alligator whosebody length is 7 feet?

Answer 1

By definition, the equation of a Direct variation has the following form:

`y=kx`

Where "k" is the constant of variation.

In this case you know that "T" represents the alligator's tail length (in feet) and "B" represents its body length.

Then, the equation for this situation has this form:

`T=kB`

According to the information given in the exercise, when:

`B=2ft`

The value of "T" is:

`T=1.4ft`

With these values, you can find "k" as following:

`\begin{gathered} T=kB \\ 1.4ft=k(2ft) \\ \\ (1.4ft)/(2ft)=k \\ \\ k=0.7 \end{gathered}`

Knowing "k", you can set up the following equation for this situation:

`T=0.7B`

If an alligator has a body length of:

`B=7ft`

You need to substitute this value into the equation and then evaluate, in order to find the corresponding value of "T". Then, you get:

`\begin{gathered} T=0.7B \\ T=0.7(7ft) \\ T=4.9ft \end{gathered}`

The answer is:

`4.9ft`