Question 32

# At a college football game, $$\frac{4}{5}$$ of the seats in the lower deck of the stadium were sold. If $$\frac{1}{4}$$ of all the seating in the stadium is located in the lower deck, and if $$\frac{2}{3}$$ of all the seats in the stadium were sold, then what fraction of the unsold seats in the stadium was in the lower deck?

Solution

Let the number of seats in the stadium = x

Number of seats in the lower deck = a and the number of seats in the upper deck be b

x=a+b

a=$$\ \frac{\ x}{4}$$ and b = $$\ \frac{\ 3x}{4}$$

Now in the lower deck $$\ \frac{\ 4a}{5}$$ seats were sold and $$\ \frac{\ a}{5}$$ seats were unsold.

Number of total seats sold in the stadium = $$\ \frac{\ 2x}{3}$$

Number of unsold seats in the lower deck =  $$\ \frac{\ a}{5}$$ =  $$\ \frac{\ x}{20}$$

Number of unsold seats in the stadium =  $$\ \frac{\ x}{3}$$

Required fraction = $$\ \frac{\ \ \frac{\ x}{20}}{\ \frac{\ x}{3}}$$

= $$\ \frac{\ 3}{\ \ 20}$$

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