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Eve, Jack and Ling share some money in the ratio 2 : 3 : 4 - OCR - GCSE Maths - Question 23 - 2023 - Paper 1
Question 23
Eve, Jack and Ling share some money in the ratio 2 : 3 : 4. Jack gets £720. Work out how much Ling gets. (b) Amir, Beth and Casey share some money in the ratio 3 :... show full transcript
Worked Solution & Example Answer:Eve, Jack and Ling share some money in the ratio 2 : 3 : 4 - OCR - GCSE Maths - Question 23 - 2023 - Paper 1
Step 1
Work out how much Ling gets.
Answer
To find how much Ling gets, we first need to determine the total parts in the ratio. The ratio for Eve, Jack, and Ling is:
- Eve: 2 parts
- Jack: 3 parts
- Ling: 4 parts
Total parts = 2 + 3 + 4 = 9 parts.
Since Jack gets £720, we know that 3 parts equal £720. Therefore, the value of each part is:
[ \text{Value of each part} = \frac{720}{3} = 240 ]
Now, we can find out how much Ling gets, which is 4 parts:
[ \text{Ling's share} = 4 \times 240 = 960 ]
Thus, Ling gets £960.
Step 2
Find the value of c.
Answer
Let the total amount of money be represented as T. According to the problem, the shares of Amir, Beth, and Casey are in the ratio 3:5:c.
The total parts in the ratio is:
3 (Amir) + 5 (Beth) + c (Casey) = 8 + c.
Since Casey's share is ( \frac{2}{3} ) of the total, we can express Casey's share in terms of T:
[ \text{Casey's share} = \frac{2}{3}T ]
From the ratio, Casey’s share can also be represented as:
[ \text{Casey's share} = \frac{c}{8+c}T ]
Setting these two equations equal to each other gives:
[ \frac{c}{8+c}T = \frac{2}{3}T ]
By cancelling T from both sides, we have:
[ \frac{c}{8+c} = \frac{2}{3} ]
Cross-multiplying gives:
[ 3c = 2(8+c) ]
Expanding this equation:
[ 3c = 16 + 2c ]
Now, isolating c:
[
3c - 2c = 16
]
[
c = 16
]
Thus, the value of c is 16.