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Sundip plans to share some money so that - Mia gets $ rac{1}{2}$ - Sara gets $ rac{2}{5}$ - Nina gets $ rac{1}{7}$ Will Sundip's plan work? Give a reason and show working to support your decision - OCR - GCSE Maths - Question 14 - 2023 - Paper 3
Question 14
Sundip plans to share some money so that - Mia gets $ rac{1}{2}$ - Sara gets $ rac{2}{5}$ - Nina gets $ rac{1}{7}$ Will Sundip's plan work? Give a reason and show w... show full transcript
Worked Solution & Example Answer:Sundip plans to share some money so that - Mia gets $ rac{1}{2}$ - Sara gets $ rac{2}{5}$ - Nina gets $ rac{1}{7}$ Will Sundip's plan work? Give a reason and show working to support your decision - OCR - GCSE Maths - Question 14 - 2023 - Paper 3
Step 1
Will Sundip's plan work?
Answer
To determine if Sundip's plan will work, we need to check if the sum of the fractions given to Mia, Sara, and Nina is less than or equal to 1.
Calculating the total fraction:
rac{1}{2} + rac{2}{5} + rac{1}{7}
We will find a common denominator, which is 70. Therefore, we convert each fraction:
- Mia: rac{1}{2} = rac{35}{70}
- Sara: rac{2}{5} = rac{28}{70}
- Nina: rac{1}{7} = rac{10}{70}
Now adding these up:
rac{35}{70} + rac{28}{70} + rac{10}{70} = rac{73}{70}
Since rac{73}{70} > 1, it indicates that Sundip's plan exceeds the total available money. Thus, Sundip’s plan will not work.
The reason is that the total fractions exceed 1.
Step 2
Work out how much money Sara gets.
Answer
Mia is set to receive £320, which represents rac{1}{2} of the total amount of money.
Let the total amount of money be denoted as . From the information given:
rac{1}{2} T = 320
To find , we rearrange this equation:
Now we know the total amount of money is £640.
To find out how much Sara gets, we use her fraction, which is rac{2}{5}:
ext{Sara's amount} = rac{2}{5} imes 640 = 256
Hence, Sara gets £256.