Tsidi needs a bookshelf to store her files - NSC Mathematical Literacy - Question 3 - 2021 - Paper 2
Question 3
Tsidi needs a bookshelf to store her files. She decides to buy a second-hand wooden bookshelf with two shelves, as illustrated below.
DIMENSIONS:
Inside width 162 c... show full transcript
Worked Solution & Example Answer:Tsidi needs a bookshelf to store her files - NSC Mathematical Literacy - Question 3 - 2021 - Paper 2
Step 1
3.1.1 Determine A, the outside length of the bookshelf.
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Answer
To find A, add the thickness of the top shelf to the inside width:
A=162extcm+1.5extcm+1.5extcm=165extcm
Step 2
3.1.2 Determine B, the inside height of the top shelf.
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Answer
To find B, subtract the thickness of the bottom shelf and the top shelf from the total outside height:
B=80extcm−(40extcm+4.5extcm+1.5extcm)=34extcm
Step 3
3.2 Determine (rounded to TWO decimal places) the conversion factor for the height in the form 1 inch = ... cm.
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To convert from inches to centimeters, divide the total outside height in centimeters by the total height in inches:
1 ext{ inch} = rac{80 ext{ cm}}{31,496 ext{ inches}} ext{ cm} \\ ext{This simplifies to } 0.0254 ext{ cm per inch.}
Step 4
3.3.1 Calculate (in cm²) the area of one side of the backboard.
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The area of one side of the backboard can be found using the formula for the area of a rectangle:
3.3.4 Verify, with calculations, whether her statement is valid.
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One 500 mL can is equivalent to 0.5 litres. Since 0.19 litres is less than 0.5 litres, Tsidi's statement is valid for painting the backboard completely.
Step 8
3.4.1 Determine the maximum number of filing boxes that can fit on one shelf, which is 162 cm wide.
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3.4.2 Calculate the difference in the number of files that she can place on one shelf if she packs the shelf with single files rather than the filing boxes.
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Answer
For single files:
Now, calculate the difference:
Step 10
3.4.3 Give a possible reason why Tsidi would prefer the filing boxes.
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Using filing boxes helps to keep documents organized and easily accessible, preventing them from getting damaged or lost.
Step 11
3.4.4 Determine, as a percentage to TWO decimal places, the probability that the file she chooses will contain the documents she is looking for.
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The probability is given by the number of items of interest (files) divided by the total number of items (all files in boxes):
ext{Probability} = rac{1}{20} imes 100 = 5 ext{.}00 ext{ \\ rounded to TWO decimal places.}
