LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!

• PRACTICE (online exercises and printable worksheets)

This lesson draws on and extends the concepts from the preceding lesson, Direct and Inverse Variation.

A Typical Proportionality Problem;
Finding the Constant of Proportionality

QUESTION:

Write an equation for:
‘$A\,$ is proportional to the square of $\,t\,$, and inversely proportional to the cube of $\,x\,$’

If $\,A = 3\,$ when $\,t = 1\,$ and $\,x = 2\,$, find the constant of proportionality.

What is the value of $\,A\,$ when $\, t = -1\,$ and $\,x = 4\,$?

SOLUTION:

$\displaystyle A = k\cdot \frac{t^2}{x^3}$	Write the equation that describes the relationship between the variables, using the information from Direct and Inverse Variation. Don't forget the constant of proportionality!
$\displaystyle 3 = k\cdot\frac{1^2}{2^3}\,$,     $\displaystyle 3 = \frac{k}{8}$	substitute the known values of $\,A\,$, $\,t\,$ and $\,x\,$; simplify
$k = 24$	solve for the constant of proportionality, $\,k\,$
$\displaystyle A = 24\cdot\frac{t^2}{x^3}\,$,     $\displaystyle A= \frac{24t^2}{x^3}$	the final equation can be written in slightly different ways
$\displaystyle A = \frac{24\cdot (-1)^2}{4^3} = \frac{24}{64} = \frac{3}{8}$	now, whenever any two of the three variables are known, the remaining variable can be determined

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.