A local lumberyard takes in $24,000 in a 12 hour period. Write a direct variation equation between the income and the number of hours.

Question

Variation word problem for my class.

Answer 1

In a direct variation one variable (y) is a constant multiple of the other (x).  When one variable changes the other changes in proportion to the first.  A direct variation equation is of the form y = kx, where k is a constant.  If you have one set of points, you can find the value of the constant k = y/x.  In this problem, let y = income earned by the lumber yard and x = hours.  We have one point, (x=12, y=$24,000)  Hence:

 

k = $24,000/12 hours = 2

 

So the direct variation equation is:

 

y = 2x