Question

The total number of fence posts Edwin installs varies directly with the number of hours worked. He installs 40 fence posts in 8 hours.

Write a direct variation equation to represent this relationship.

Answer 1

y = 5x

where

y = number of fence posts that Edwin installs
x = number of hours that Edwin takes to install y posts

Explanation:

Let y = number of fence posts that Edwin installs in x hours

We have the relation:

y ∝ x where ∝ is the symbol for is-proportional-to

We can rewrite this as an equation using the constant of proportionality,k:

y =kx

Given y = 40 fences, x = 8 hours we get

40 = k(8) = 8k

or, switching sides

8k = 40

k = 40/8 = 5

So Edwin can install 5 fences per hour

Plugging this into the equation of proportionality

y = 5x