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Anne, Barry and Colin share a prize in the ratio 3 : 4 : 5 - OCR - GCSE Maths - Question 19 - 2019 - Paper 1
Question 19
Anne, Barry and Colin share a prize in the ratio 3 : 4 : 5. Colin gives \( \frac{1}{3} \) of his share to a charity. What fraction of the whole prize does Colin give... show full transcript
Worked Solution & Example Answer:Anne, Barry and Colin share a prize in the ratio 3 : 4 : 5 - OCR - GCSE Maths - Question 19 - 2019 - Paper 1
Step 1
What fraction of the whole prize does Colin give to the charity?
Answer
To solve this, we first need to determine the total parts from the ratio:
- Anne's parts: 3
- Barry's parts: 4
- Colin's parts: 5
Total parts = 3 + 4 + 5 = 12 parts.
Colin's share of the prize can be represented as:
[ \text{Colin's share} = \frac{5}{12} \text{ of the total prize} ]
Colin gives ( \frac{1}{3} ) of his share to charity, which is:
[ \text{Charity contribution} = \frac{1}{3} \times \frac{5}{12} = \frac{5}{36} \text{ of the total prize} ]
Thus, the fraction of the whole prize that Colin gives to the charity is ( \frac{5}{36} ).
Step 2
How much money did they share?
Answer
In the ratio 5 : 7 : 8, let the total money shared be represented as:
[ 5x + 7x + 8x = 20x ]
Freya's share is given as £1600, which corresponds to 8 parts in the ratio. Therefore, we can derive the value of ( x ):
[ 8x = 1600 \Rightarrow x = \frac{1600}{8} = 200 ]
Now, we can calculate the total money shared:
[ 20x = 20 \times 200 = 4000 ]
Thus, the total amount of money they shared is £4000.