Answer:
145.31 ft2
Explanation:
The fraction painted by the painter is an absolute value when the fraction is applied to the total area of the wall.
Total area = 150 ft2
He decides to paint half of the wall and then take a break. This means that he painted
= 1/2 × 150 ft2
=75 ft2
Area left unpainted = 150 ft2 - 175 ft2 = 75 ft2
After his break, he paints half of the remaining unpainted portion, This means that he painted
= 1/2 × 75 ft2
=37.5 ft2
Area left unpainted = 75 ft2 - 37.5 ft2 = 37.5 ft2
At this rate, the portion unpainted after the 5th break can be so determined;
a = 150 where a is the original area unpainted
r = common ratio = 1/2 ( the rate of painting as a function of the area)
Area unpainted after first break = ar = 150 × 1/2 = 75 ft2
Area unpainted after the second break = ar^2 = 150(1/2)^2 = 37.5 ft2
Thus area unpainted after the 5th break
=ar^5 = 150(1/2)^5 = 4.6875
Portion of the original wall will be painted when he takes his fifth break
= 150 - 4.6875
= 145.3125 ft2