Chapter 13.3, Problem 41STP

To determine

To explain:

The expression that gives the number of gallons of paint that Miki needs to buy to paint her room.

Answer to Problem 41STP

The expression that gives the number of gallons of paint that Miki needs to buy to paint her room is $\left(F\right)$ $=\frac{\left(x+6\right)}{\left(x+4\right)}$ .

Explanation of Solution

Given information:

Room area: $x^2+8x+12$

One gallon of paint covers: $x^2+6x+8$

Calculation:

A room has an area of square feet, and one gallon of paint covers square feet. To find out how many gallons of paint is needed to paint the entire room, divide the total square feet by the number of feet that a gallon covers as follows:

  $\begin{array}{l}Gallonsneeded=\frac{x^2+8x+12}{x^2+6x+8}\\ Gallonsneeded=\frac{\left(x+6\right)\left(x+2\right)}{\left(x+4\right)\left(x+2\right)}\\ Gallonsneeded=\frac{\left(x+6\right)}{\left(x+4\right)}\end{array}$

Thus, the correct answer is $\left(F\right)$ $=\frac{\left(x+6\right)}{\left(x+4\right)}$ .