Each day, Eve records how long it takes her to complete a puzzle - OCR - GCSE Maths - Question 10 - 2020 - Paper 1
Question 10
Each day, Eve records how long it takes her to complete a puzzle.
On Friday, she took 50% less time than Thursday.
On Saturday, she took 20% less time than on Frida... show full transcript
Worked Solution & Example Answer:Each day, Eve records how long it takes her to complete a puzzle - OCR - GCSE Maths - Question 10 - 2020 - Paper 1
Step 1
Step 1: Determine the time taken on Saturday
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Answer
Eve completes the puzzle on Saturday in 36 minutes. Let the time taken on Friday be denoted as F minutes.
Step 2
Step 2: Determine the time taken on Friday in relation to Thursday
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Answer
According to the information given, she took 50% less time on Friday than on Thursday. This can be expressed as:
F=T−0.5T=0.5T
where T is the time taken on Thursday.
Step 3
Step 3: Determine the time taken on Saturday in relation to Friday
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Answer
On Saturday, Eve took 20% less time than on Friday. Therefore, the equation is:
36=F−0.2F=0.8F.
Step 4
Step 4: Substitute F from Step 2 into Step 3
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Answer
Substituting the expression for F gives us:
36=0.8(0.5T).
This simplifies to:
36=0.4T.
Step 5
Step 5: Solve for T
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Answer
To find the time taken on Thursday, T, rearranging the equation yields:
T=0.436=90.
Thus, Eve took 90 minutes to complete the puzzle on Thursday.
