4 At the end of 2017
the value of Tamara's house was $£ 220000$
the value of Rahim's house was $£ 160000$
At the end of 2019
the value of Tamara's house had decreased by $20 \%$ the value of Rahim's house had increased by $30 \%$
At the end of 2019 , whose house had the greater value? You must show how you get your answer.
Answer
\(\boxed{\text{At the end of 2019, Rahim's house had the greater value}}\)
Step 1 ：Let's find the value of Tamara's house at the end of 2019 by decreasing its value by 20\%. So, \(220000 - 0.20 \times 220000 = 220000 \times (1 - 0.20) = 220000 \times 0.80 = 176000\)
Step 2 ：Let's find the value of Rahim's house at the end of 2019 by increasing its value by 30\%. So, \(160000 + 0.30 \times 160000 = 160000 \times (1 + 0.30) = 160000 \times 1.30 = 208000\)
Step 3 ：Comparing the values of their houses at the end of 2019, we have Tamara's house at \(£176000\) and Rahim's house at \(£208000\)
Step 4 ：\(\boxed{\text{At the end of 2019, Rahim's house had the greater value}}\)
