1. ## maximum area

The crawleys hallway has 300ft² of wall space. They recived an estimate of $1.40/ft² to paint a wall and 60˘/ft² to wallpaper a wall. With$324 to spend, what is the maximum area they can have painted if the rest has to be papered.

I would greatly appreciate any help.

2. Originally Posted by begold91
The crawleys hallway has 300ft² of wall space. They recived an estimate of $1.40/ft² to paint a wall and 60˘/ft² to wallpaper a wall. With$324 to spend, what is the maximum area they can have painted if the rest has to be papered.

I would greatly appreciate any help.
$\displaystyle p=1\text{ft.}^2\text{ of paint}$
$\displaystyle w=1\text{ft.}^2\text{ of wallpaper}$

The price of the whole thing is: $\displaystyle 1.4p+0.6w\leq324$

And: $\displaystyle p+w=300$

So: $\displaystyle w=300-p$

Go back to the price equation: $\displaystyle 1.4p+0.6w\leq324$

Substitute: $\displaystyle 1.4p+0.6(300-p)\leq324$

Multiply: $\displaystyle 1.4p+180-0.6p\leq324$

Group like terms: $\displaystyle 1.4p-0.6p+180\leq324$

Subtract: $\displaystyle 0.8p+180\leq324$

Subtract 180 from both sides: $\displaystyle 0.8p\leq144$

Divide both sides by 0.8: $\displaystyle \boxed{p\leq180}$