Photo AI
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 the ratio of 2 : 3 implies that the total parts of money is 2 + 3 = 5 parts.
Hannah's share, which is represented by the '2' in the ratio, actually corresponds to ( \frac{2}{5} ) of the total money, not ( \frac{2}{3} ). Thus, ( \frac{2}{3} ) of the total money represents more than half of the sum, which contradicts the given ratio.
Step 2
Write the ratio of the money that Siobhan receives to the money that Iwan receives.
Answer
Let Siobhan's share be represented as ( x ). Since Iwan receives ( \frac{11}{17} ) of the total money, Siobhan receives the remainder, which can be calculated as follows:
Siobhan's share = Total money - Iwan's share = ( 1 - \frac{11}{17} = \frac{6}{17} ).
The ratio of Siobhan's to Iwan's money is thus: [ 6 : 11 ].