Question

Angie cleans 1/3 of the yard. Alex Cleans 1/4 of the remaining. What fraction of the yard is left Unclean?
​

Answer 1

Answer:

Let area of yard be x.

$Yard \: clean \: by \: Angle = \frac{x}{3} </p><p> \\ Yard \: clean \: by \: Alex = \: \frac{x}{4} </p><p> \\ portion \: of \: Yard \: remains \: unclean \: = x - \frac{x}{3} - \frac{x}{4} \\ = \frac{12x - 4x - 3x}{12} \\ = \frac{5x}{12} \\ Fraction \: of \: yard \: remain \: uncleaned \: is \frac{5}{12}$

Answer 2

Given: Area of the yard cleaned by Angie = 1/3

           Area cleaned by Alex = 1/4 of the remaining

To find: Fraction of the yard that is left unclean

Let: Area of the yard = Y units

Solution: According to the given question and assumption made,

If total area of yard is Y units and Angie cleans 1/3 of it, then

Area cleaned by Angie = $\frac{1}{3}$ × Y = $\frac{Y}{3}$

Remaining area = Total area of yard - area cleaned by Angie

                           = Y - $\frac{Y}{3}$ = $\frac{3Y - Y}{3}$ = $\frac{2Y}{3}$

Area cleaned by Alex = 1/4 of the remaining area

                                    = $\frac{1}{4}$ × $\frac{2Y}{3}$

                                    = $\frac{2Y}{12}$ or $\frac{Y}{6}$

Area of the yard left uncleaned = Total area - Area cleaned by Angie and Alex

                       = Y - (Area cleaned by Angie + Area cleaned by Alex)

                       = Y - ($\frac{Y}{3}$ + $\frac{Y}{6}$)

                       = Y - ($\frac{2Y + Y}{6}$)

                       = Y - $\frac{3Y}{6}$ = $\frac{6Y - 3Y}{6}$ = $\frac{3Y}{6}$   OR  $\frac{Y}{2}$

The fraction of the yard that is left unclean is 1/2.