Video: US-SAT05S4-Q03-894189506328v2

A wall in a room that is approximately 7 3/4 ft wide was covered with 20 strips of wallpaper of equal width, laid side by side. Which of the following is closest to the number of strips of wallpaper laid side by side needed to cover a wall of width 24 ft? [A] 50 [B] 70 [C] 60 [D] 30

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Video Transcript

A wall in a room that is approximately seven and three-quarters feet wide was covered with 20 strips of wallpaper of equal width, laid side by side. Which of the following is closest to the number of strips of wallpaper laid side by side needed to cover a wall of width 24 feet? Is it A) 50, B) 70, C) 60, or D) 30?

As we’re dealing with approximations and we’re looking for the closest answer, we don’t need to work out the exact values. Let’s firstly consider the information we were given in the question. We know that a wall approximately seven and three-quarters feet wide can be covered with 20 strips of wallpaper. Seven and three-quarters feet rounded to the nearest foot is equal to eight feet. We can, therefore, assume that a wall of width eight feet could also be covered with approximately 20 strips.

We need to calculate the number of strips of wallpaper required for a wall of width 24 feet. Eight multiplied by three is equal to 24. This means that we also need to multiply the number of strips by three. 20 multiplied by three is equal to 60. As 60 was one of our four options, this is the correct answer. Option C is correct.

We could have tried to find a more accurate answer by working out how many strips of wallpaper are needed for one foot first. Seven and three-quarter feet is the same as 7.75 feet. Dividing this by 7.75 gives us one foot. We need to divide 20 by the same value. 20 divided by 7.75 is equal to 2.5806 and so on. This means that we can cover one foot of the wall with 2.5806 strips of wallpaper.

In order to calculate how many strips are required for 24 feet, we need to multiply this by 24. 2.5806 multiplied by 24 is equal to 61.935, etcetera. This means that we need approximately 62 strips to cover a wall of width 24 feet. Our four options were 50, 70, 60, and 30. The number that is closest to 62 is 60. We have once again proved that the number that is closest is option C 60 strips.

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