The width, w, of a kitchen cupboard is 60 cm, correct to the nearest centimetre - OCR - GCSE Maths - Question 9 - 2021 - Paper 1
Question 9
The width, w, of a kitchen cupboard is 60 cm, correct to the nearest centimetre.
(a) Complete the error interval for the width, w.
(b) Six of these kitchen cupboar... show full transcript
Worked Solution & Example Answer:The width, w, of a kitchen cupboard is 60 cm, correct to the nearest centimetre - OCR - GCSE Maths - Question 9 - 2021 - Paper 1
Step 1
Complete the error interval for the width, w.
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Answer
The width is given as 60 cm, correct to the nearest cm. This means the actual width, w, can range from 59.5 cm to 60.5 cm.
Thus, the error interval for w is:
59.5extcmextextextextextextext<w<60.5extcm
Step 2
Show that the six cupboards may not fit along the wall.
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Answer
Each cupboard has a maximum width of 60.5 cm. Therefore, for six cupboards, the total maximum width is:
extTotalWidth=6imes60.5extcm=363extcm
Since the total length of the wall is also 363 cm, this indicates that the cupboards may not fit because they could exceed the wall length if even one cupboard is greater than the assumed maximum width.
Step 3
Find the upper bound of the space remaining if six cupboards do fit along the wall.
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Answer
Using the minimum width of the cupboards (59.5 cm), the total width for six cupboards is:
extTotalWidth=6imes59.5extcm=357extcm
The length of the wall is 363 cm, so the space remaining is:
extRemainingSpace=363extcm−357extcm=6extcm
The upper bound of the space remaining, when the cupboards do fit, is 6 cm.
