Question

if 1/4 of a gallon of paint is needed to paint 2/3 of a fence, how many gallons are needed to paint the entire fence? site:socratic.org

Answer 1

Answer:3/8 gallons of paint is needed to paint the entire fence.

Step-by-step explanation:

Let x represent the entire area of the fence that is to be painted.

If 1/4 of a gallon of paint is needed to paint 2/3 of a fence, it means that 1/4 of a gallon of paint is needed to paint 2x/3

The number of gallons needed to paint the entire fence would be

(x/4)/(2x/3) = x/4 × 3/2x = 3/8 gallons

Answer 2

$\bf \begin{array}{ccll} \stackrel{paint}{gallons}&fence\\ \cline{1-2} \\\frac{1}{4}&\frac{2}{3}\\\\ x&1 \end{array}\implies \cfrac{~~\frac{1}{4}~~}{x}=\cfrac{~~\frac{2}{3}~~}{1}\implies \cfrac{~~\frac{1}{4}~~}{\frac{x}{1}}=\cfrac{2}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{x}=\cfrac{2}{3} \\\\\\ \cfrac{1}{4x}=\cfrac{2}{3}\implies 3=8x\implies \cfrac{3}{8}=x$