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Elise wants to divide a sum of money between Hannah and Adil in the ratio 2 : 3 - OCR - GCSE Maths - Question 9 - 2018 - Paper 1
Question 9
Elise wants to divide a sum of money between Hannah and Adil in the ratio 2 : 3. Elise says: Hannah will get \( \frac{2}{3} \) of the money. Explain why Elise is ... show full transcript
Worked Solution & Example Answer:Elise wants to divide a sum of money between Hannah and Adil in the ratio 2 : 3 - OCR - GCSE Maths - Question 9 - 2018 - Paper 1
Step 1
Explain why Elise is not correct.
Answer
Elise is incorrect because she states that Hannah will receive ( \frac{2}{3} ) of the total money. However, based on the ratio 2:3, the total parts are 2 + 3 = 5. Therefore, Hannah's share should actually be ( \frac{2}{5} ) of the money, which is less than half. Hence, ( \frac{2}{3} ) is not a valid representation of Hannah's share in this context.
Step 2
Write the ratio of the money that Siobhan receives to the money that Iwan receives.
Answer
Given that Iwan receives ( \frac{11}{17} ) of the total money, Siobhan's share can be calculated as follows:
Since Iwan receives ( \frac{11}{17} ), it means that Siobhan receives the remaining amount. Thus:
[ \text{Siobhan's share} = 1 - \frac{11}{17} = \frac{6}{17} ]
Now, the ratio of Siobhan's money to Iwan's money is:
[ \text{Ratio} = \frac{\text{Siobhan's money}}{\text{Iwan's money}} = \frac{6/17}{11/17} = \frac{6}{11} ]
Therefore, the required ratio is ( 6 : 11 ).