In 2017, the value of a house increased by 4% - OCR - GCSE Maths - Question 10 - 2019 - Paper 6
Question 10
In 2017, the value of a house increased by 4%.
In 2018, the value of the house then decreased by 3%.
Teresa says
Over the two years the value of the house increased... show full transcript
Worked Solution & Example Answer:In 2017, the value of a house increased by 4% - OCR - GCSE Maths - Question 10 - 2019 - Paper 6
Step 1
Calculate the value after a 4% increase in 2017
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Answer
Let the initial value of the house in 2017 be represented by V. After a 4% increase, the new value becomes:
V2017=V+0.04V=1.04V.
This is the value of the house at the end of 2017.
Step 2
Calculate the value after a 3% decrease in 2018
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Answer
In 2018, the value then decreases by 3%. The value after this decrease is:
V2018=V2017−0.03V2017=1.04V−0.03(1.04V)=1.04V(1−0.03)=1.04V(0.97)=1.0088V.
Thus, the value of the house at the end of 2018 is 1.0088V.
Step 3
Calculate the overall percentage change
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Answer
The overall change in value from the initial V to the new value 1.0088V can be calculated as follows:
Determine the increase: 1.0088V−V=0.0088V.
Calculate the percentage increase:
ext{Percentage Increase} = rac{0.0088V}{V} imes 100 ext{%} = 0.88 ext{%}.
Thus, the total increase over the two years is 0.88%, not the 1% that Teresa claims.
Step 4
Conclusion
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Answer
Therefore, Teresa is wrong as the value of the house actually increased by 0.88% over the two years, not 1%.
