Question

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?

112.50 ft2

145.31 ft2

147.66 ft2

290.63 ft2

Answer 1

By the fifth break, the painter will have painted approximately 145.31 ft2 of the original wall, calculated by summing the areas painted after each break using a geometric sequence.

Step-by-step explanation:

The question asks for the amount of wall painted after each successive break if the painter paints half of the remaining unpainted portion each time. By the fifth break, the painter will have painted a specific portion of the wall using a geometric sequence to represent the remaining unpainted area after each break.

Initially, the area of the wall is 150 ft2. After each break, half of the remaining area is painted. The sequence of areas painted is as follows:

First break, 1/2 painted : 150 ft2 / 2 = 75 ft2 painted, 75 ft2 left

Second break, 1/2 of the remaining painted: 75 ft2 / 2 = 37.5 ft2 painted, 37.5 ft2 left

Third break, 1/2 of the remaining painted: 37.5 ft2 / 2 = 18.75 ft2 painted, 18.75 ft2 left

Fourth break, 1/2 of the remaining painted: 18.75 ft2 / 2 = 9.375 ft2 painted, 9.375 ft2 left

Fifth break, 1/2 of the remaining painted: 9.375 ft2 / 2 = 4.6875 ft2 painted

Adding up the areas painted by the fifth break: 75 + 37.5 + 18.75 + 9.375 + 4.6875 = 145.31 ft2. Therefore, approximately 145.31 ft2 of the original wall will have been painted by the time the painter takes his fifth break.

Answer 2

The painter would have 145.3125 ft^2 painted after the fifth break.