Eve, Jack and Ling share some money in the ratio 2 : 3 : 4 - OCR - GCSE Maths - Question 3 - 2023 - Paper 4

For the second part of the question, Amir, Beth, and Casey share money in the ratio 3:5:c. We need to find the value of c given that Casey’s share is \frac{2}{3} of the total amount.

First, let the total amount be represented as T. The parts for Amir, Beth, and Casey are:

• Amir: 3 parts
• Beth: 5 parts
• Casey: c parts

The total number of parts is:

$3 + 5 + c = 8 + c$

Casey’s share is calculated as:

$\text{Casey's share} = \frac{c}{8+c} \times T$

Given that Casey's share is also \frac{2}{3} of T, we set the equations equal to each other:

$\frac{c}{8+c} \times T = \frac{2}{3}T$

We can cancel T from both sides (assuming T ≠ 0):

$\frac{c}{8+c} = \frac{2}{3}$

Now we cross-multiply:

$3c = 2(8+c)$

Simplifying this we get:

\Rightarrow c = 16$$ Therefore, the value of c is 16.