An artist purchased 24 high quality canvases to be used for painting this fall. Each week she will allow herself to use three of the canvases for painting until all 24 canvases have been used. Write a linear equation modelling the number of canvases remaining (y) as a function of weeks painting (x).

canvases over weeks

Step-by-step explanation:

Given:

w(h) represents how many hours per week

c(t) approximates how many canvases she paints per hour

In function composition, if we have two function f(x) and g(x) then

(f.g)(x) or f(g(x)) means first apply g(), then apply f() i.e. applying function f to the results of function g.

Now we have c(w(h)), this means first we apply w(h) which will give us hours per week and then we'll apply function 'c' on the results of 'w' (that is number of hours for weeks painted). As result we'll get number of canvas per week!

Remove the parentheses from the equation:

Combine like terms:

The greatest common factor (GCF) of both terms is 8, so we can divide the entire expression by 8 and move it outside parentheses:

The simplified form of this expression is 8(r - 1).